Analysis_Workflow_Fish
Catarina Pien
3/25/2020
Preparation
Load Packages
Import data
- This is a dataset of fish catch for the North Delta Flow Action.
- Merge flow data into rest of data
- Define variable structures
- Order action phases
- Regional assignments
Fish_ndfa <- read.csv("Data/FISH_MAN_allIEPsurveys_20200527.csv")
FlowDesignation <- read.csv("Data/FlowDatesDesignations.csv")
Regions <- read.csv("Data/Stations_Fish_NDFA_2020-05-28.csv")
# Look at data
head(Fish_ndfa)
str(Fish_ndfa)
# Add variables
Fish_ndfa$Date <- ymd(Fish_ndfa$Date)
Fish_ndfa$Month <- month(Fish_ndfa$Date)
Fish_ndfa$Day <- day(Fish_ndfa$Date)
Fish_ndfa$Year <- ordered(Fish_ndfa$Year)
FlowDesignation$Year <- ordered(FlowDesignation$Year)
FlowDesignation$PreFlowStart <- mdy(FlowDesignation$PreFlowStart)
FlowDesignation$PreFlowEnd <- mdy(FlowDesignation$PreFlowEnd)
FlowDesignation$PostFlowStart <- mdy(FlowDesignation$PostFlowStart)
FlowDesignation$PostFlowEnd <- mdy(FlowDesignation$PostFlowEnd)
# Merge data from FlowDesignation Table (Water Year Type, Flow days and type)
# Filter only Pre-During-Post Flow Action Data.
# We have a during action, and then Pre = 30 days before/Post = 30 days after
Fish_all0 <- inner_join(Fish_ndfa,FlowDesignation, by = "Year")
Fish_all1 <- left_join(Fish_all0, Regions)
Fish_all <- Fish_all1 %>%
mutate(ActionPhase = ifelse(Date > PreFlowStart & Date<PreFlowEnd, "Pre", NA)) %>%
mutate(ActionPhase = replace(ActionPhase, Date > PreFlowEnd & Date < PostFlowStart, "During")) %>%
mutate(ActionPhase = replace(ActionPhase, Date > PostFlowStart & Date < PostFlowEnd, "Post")) %>%
filter(!is.na(ActionPhase)) %>%
select(-c(PreFlowStart:PostFlowEnd)) %>%
arrange(Date, Survey, StationCode, CommonName)
# Order Action Phases
Fish_all$ActionPhase <- as.factor(Fish_all$ActionPhase)
Fish_all$ActionPhase <- factor(Fish_all$ActionPhase, levels(Fish_all$ActionPhase)[c(3,1,2)])
# Define variable structures
Fish_all$Date <- ymd(Fish_all$Date)
Fish_all$Month <- ordered(Fish_all$Month)
Fish_all$Year <- ordered(Fish_all$Year)
Fish_all$WYType <- as.factor(Fish_all$WYType)
Fish_all$ActionPhase <- as.factor(Fish_all$ActionPhase)
Fish_all$X1 <- NULLPlotting Functions
## FUNCTIONS FOR PLOTTING -------------------------------------------------------------
VisPoint <- function(data,y) {
y <- enquo(y)
data %>%
ggplot() +
geom_point(mapping = aes(Date,!! y), size = 2) +
theme_bw() +
scale_colour_manual(values = c("coral3", "lightseagreen"))+
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.border = element_blank(),
axis.line = element_line(colour = "black"),
plot.title = element_text(hjust=0.5),
axis.text = element_text(size = 11),
axis.text.x = element_text(angle = 90, hjust = 1),
axis.title = element_text(size = 12),
legend.text = element_text(size = 11),
legend.position = "bottom")
}
# Boxplots by variable of interest
VisBox <- function(data, x, y) {
x <- enquo(x)
y <- enquo(y)
data %>%
ggplot() +
geom_boxplot(mapping = aes(!! x,!! y), fill = "lightseagreen", colour = "lightgray") +
theme_bw() +
scale_colour_manual(values = c("coral3", "lightseagreen"))+
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.border = element_blank(),
axis.line = element_line(colour = "black"),
plot.title = element_text(hjust=0.5),
axis.text = element_text(size = 11),
axis.text.x = element_text(angle = 90, hjust = 1),
axis.title = element_text(size = 12),
legend.text = element_text(size = 11))
}
#----------------------------------------------------------------------------------------------------
####################################################################################################Exploration of overall dataset
- Station distribution
- Time span
- Number of fish per survey
- Total counts per survey
- Locations
library(leaflet)
library(plotly)
# Look at locations
# Define palette
pal <- colorFactor(c("slateblue", "darkseagreen", "orange", "orangered", "hotpink"), domain = c("DJFMP", "Yolo", "Townet", "EDSM", "FMWT"))
leaflet(Fish_all) %>%
addTiles() %>%
addCircleMarkers(
color = ~pal(Survey),
opacity = 0.5,
lng = ~Longitude,
lat = ~Latitude,
label = ~StationCode) %>%
addLegend(pal = pal,
values = ~Survey,
position = "bottomright")# Time span
time <- Fish_all%>%
group_by(Survey, Year) %>%
summarize(sum.count = sum(totalCount))
ggplot(time, aes(x = Survey, y = Year, fill = sum.count)) + geom_tile() + theme_minimal()
# Look at datasets
Fishsp <- Fish_all %>%
group_by(CommonName) %>% summarize(count = n())
Fish_all %>%
plot_ly(x = ~Survey,
y = ~totalCount,
type = "box")Fishsp %>%
plot_ly(x = ~CommonName,
y = ~count,
type = "bar")Datasets by fish type
- Make some lists of datasets you might want to filter from the big dataset
Seine Data
Data Prep
- Filter to just seine data
- Fill in zeros for unlisted species
- Calculate CPUE
- Organize data the way you want it
### Complete Cases
# For each Date, Survey, StationCode combination, make sure each fish species is represented with
# either positive count or zero.
Seine_completecase <- Seine %>%
group_by(Date, Survey, StationCode, CommonName) %>%
summarize(sum.count = sum(totalCount)) %>%
ungroup() %>%
complete(CommonName, nesting(Date, Survey, StationCode), fill = list(sum.count = 0)) %>%
arrange(Date,Survey, StationCode,CommonName)
### Merge back together with rest of data
# Get distinct samples for looking at Water Quality
Seine_samples <- Seine %>% select(-c(CommonName, totalCount)) %>% distinct()
# Merge
Seine_complete <- left_join(Seine_completecase, Seine_samples, by = c("Date", "Survey", "StationCode"))
# There is a Yolo sample with two volumes... this is why there are more rows of Seine_complete
### Calculate CPUE
# Remove samples with no volume
Seine_CPUE <- Seine_complete %>%
filter(!is.na(VolumeSampled))%>%
mutate(CPUE = round(sum.count/VolumeSampled,2))
### Rearrange columns
Seine_f <- Seine_CPUE[, c("Date", "Year", "Month", "Day", "Survey", "StationCode",
"Latitude", "Longitude", "Region", "MethodCode",
"WYType", "FlowPulseType", "NetFlowDays","ActionPhase",
"Secchi", "Turbidity", "Conductivity", "WaterTemp", "DO", "Tow",
"Depth", "VolumeSampled", "CommonName", "sum.count", "CPUE")]
### Mean CPUE
## Calculate means for each species by year-location-actionphase
CPUE_means_seine_phase <- Seine_f %>%
group_by(Year, Survey, StationCode, ActionPhase, CommonName) %>%
summarize(mean.CPUE = mean(CPUE)) Data Exploration
Water Quality
- Simple point plots and histograms, correlation matrix
############ OUTLIERS #################
# Boxplots
WTvis1 <- VisPoint(Seine_samples, WaterTemp)
WTvis2 <- VisBox(Seine_samples, Month, WaterTemp)
WTvis3 <- VisBox(Seine_samples, Year, WaterTemp)
Cvis1 <- VisPoint(Seine_samples, Conductivity)
Cvis2 <- VisBox(Seine_samples, Month, Conductivity)
Cvis3 <- VisBox(Seine_samples, Year, Conductivity)
Svis1 <- VisPoint(Seine_samples, Secchi)
Svis2 <- VisBox(Seine_samples, Month, Secchi)
Svis3 <- VisBox(Seine_samples, Year, Secchi)
Tvis1 <- VisPoint(Seine_samples, Turbidity)
Tvis2 <- VisBox(Seine_samples, Month, Turbidity)
Tvis3 <- VisBox(Seine_samples, Year, Turbidity)
DOvis1 <- VisPoint(Seine_samples, DO)
DOvis2 <- VisBox(Seine_samples, Month, DO)
DOvis3 <- VisBox(Seine_samples, Year, DO)
# Plot together
grid.arrange(WTvis1, WTvis2, WTvis3, Cvis1, Cvis2, Cvis3, Svis1, Svis2, Svis3,
Tvis1, Tvis2, Tvis3, DOvis1, DOvis2, DOvis3, ncol = 3)
# Boxplots
plot_ly(data = Seine_samples, x = ~StationCode, y = ~WaterTemp, color = ~StationCode, type = 'box')plot_ly(data = Seine_samples, x = ~StationCode, y = ~Conductivity, color = ~StationCode, type = 'box')plot_ly(data = Seine_samples, x = ~StationCode, y = ~Secchi, color = ~StationCode, type = 'box')plot_ly(data = Seine_samples, x = ~StationCode, y = ~Turbidity, color = ~StationCode, type = 'box')plot_ly(data = Seine_samples, x = ~StationCode, y = ~DO, color = ~StationCode, type = 'box')############ CORRELATIONS ####################
# Correlation Matrix WQ
Corr.wq <- Seine_samples %>% select(WaterTemp, Conductivity, Secchi, Turbidity, DO)
ggpairs(Corr.wq)
# Variance Inflation Factor (VIF)
corvif(Corr.wq) # Want to get rid of the variable if VIF > 4##
##
## Variance inflation factors
##
## GVIF
## WaterTemp 1.108283
## Conductivity 1.688919
## Secchi 1.566020
## Turbidity 1.484982
## DO 1.709443Clean up WQ data (QC)
- Edit anything that needs to be removed, flagged, changed.
- Replace Missing Data
# Clean up wq data
# QC Check - does anything look weird?
Seine_samples %>% filter(WaterTemp>40 | WaterTemp<1)## Date Survey StationCode MethodCode Secchi Conductivity Turbidity DO
## 1 2018-10-15 DJFMP LI004E SEIN NA 153.3 16.3 9.17
## WaterTemp Year Tow Depth VolumeSampled Latitude Longitude Month Day WYType
## 1 50.6 2018 NA 0.7 63 38.26514 -121.6716 10 15 BN
## FlowPulseType NetFlowDays Region ActionPhase
## 1 MA-Ag 30 CacheSloughComplex PostSeine_samples %>% filter(Secchi > 0.95)## Date Survey StationCode MethodCode Secchi Conductivity Turbidity DO
## 1 2011-08-31 Yolo YB BSEIN 1 1157 NA 4.03
## WaterTemp Year Tow Depth VolumeSampled Latitude Longitude Month Day WYType
## 1 20.7 2011 1 NA 172.5 38.56538 -121.631 8 31 W
## FlowPulseType NetFlowDays Region ActionPhase
## 1 NF 63 CentralYolo DuringSeine_samples %>% filter(Conductivity > 4000)## Date Survey StationCode MethodCode Secchi Conductivity Turbidity DO
## 1 2012-10-19 DJFMP MS001N SEIN NA 4112 NA 6.19
## 2 2014-08-19 DJFMP MS001N SEIN NA 4739 5.54 8.85
## 3 2014-09-05 DJFMP MS001N SEIN NA 4985 19.50 8.98
## 4 2014-09-16 DJFMP MS001N SEIN NA 4903 4.48 8.22
## 5 2014-09-30 DJFMP MS001N SEIN NA 5727 5.53 9.29
## 6 2014-10-09 DJFMP MS001N SEIN NA 7770 10.80 9.13
## 7 2015-07-23 DJFMP MS001N SEIN NA 6099 8.02 7.27
## 8 2015-08-04 DJFMP MS001N SEIN NA 7904 7.85 8.01
## 9 2015-08-11 DJFMP MS001N SEIN NA 7116 13.50 8.82
## 10 2015-08-18 DJFMP MS001N SEIN NA 5992 10.20 6.30
## 11 2015-08-25 DJFMP MS001N SEIN NA 6139 25.00 8.73
## 12 2015-09-03 DJFMP MS001N SEIN NA 6260 9.19 8.84
## 13 2015-09-17 DJFMP MS001N SEIN NA 7579 5.62 5.96
## 14 2015-09-24 DJFMP MS001N SEIN NA 8118 18.60 8.61
## 15 2015-09-29 DJFMP MS001N SEIN NA 4469 18.10 9.97
## 16 2015-10-06 DJFMP MS001N SEIN NA 7618 12.30 6.23
## 17 2015-10-14 DJFMP MS001N SEIN NA 6975 5.22 5.51
## 18 2015-10-20 DJFMP MS001N SEIN NA 6740 15.90 6.28
## 19 2015-10-27 DJFMP MS001N SEIN NA 6507 3.25 7.68
## WaterTemp Year Tow Depth VolumeSampled Latitude Longitude Month Day WYType
## 1 19.1 2012 NA 0.7 31.85 38.05604 -121.7856 10 19 BN
## 2 21.2 2014 NA 0.9 36.00 38.05604 -121.7856 8 19 C
## 3 20.9 2014 NA 0.9 28.35 38.05604 -121.7856 9 5 C
## 4 20.5 2014 NA 0.9 31.50 38.05604 -121.7856 9 16 C
## 5 20.7 2014 NA 0.8 28.80 38.05604 -121.7856 9 30 C
## 6 20.8 2014 NA 0.5 8.75 38.05604 -121.7856 10 9 C
## 7 22.8 2015 NA 0.6 13.50 38.05604 -121.7856 7 23 C
## 8 21.8 2015 NA 0.3 9.00 38.05604 -121.7856 8 4 C
## 9 22.7 2015 NA 0.8 28.80 38.05604 -121.7856 8 11 C
## 10 23.0 2015 NA 0.6 9.00 38.05604 -121.7856 8 18 C
## 11 21.0 2015 NA 0.7 29.40 38.05604 -121.7856 8 25 C
## 12 21.1 2015 NA 0.7 18.90 38.05604 -121.7856 9 3 C
## 13 20.1 2015 NA 0.5 12.00 38.05604 -121.7856 9 17 C
## 14 21.2 2015 NA 0.7 29.40 38.05604 -121.7856 9 24 C
## 15 19.6 2015 NA 0.4 3.20 38.05604 -121.7856 9 29 C
## 16 20.1 2015 NA 0.8 31.20 38.05604 -121.7856 10 6 C
## 17 20.6 2015 NA 0.5 12.50 38.05604 -121.7856 10 14 C
## 18 19.2 2015 NA 0.8 50.40 38.05604 -121.7856 10 20 C
## 19 18.6 2015 NA 0.6 21.00 38.05604 -121.7856 10 27 C
## FlowPulseType NetFlowDays Region ActionPhase
## 1 CA 38 LowerSacRiver Post
## 2 NF 15 LowerSacRiver Pre
## 3 NF 15 LowerSacRiver Pre
## 4 NF 15 LowerSacRiver During
## 5 NF 15 LowerSacRiver Post
## 6 NF 15 LowerSacRiver Post
## 7 NF 42 LowerSacRiver Pre
## 8 NF 42 LowerSacRiver Pre
## 9 NF 42 LowerSacRiver Pre
## 10 NF 42 LowerSacRiver Pre
## 11 NF 42 LowerSacRiver During
## 12 NF 42 LowerSacRiver During
## 13 NF 42 LowerSacRiver During
## 14 NF 42 LowerSacRiver During
## 15 NF 42 LowerSacRiver During
## 16 NF 42 LowerSacRiver Post
## 17 NF 42 LowerSacRiver Post
## 18 NF 42 LowerSacRiver Post
## 19 NF 42 LowerSacRiver PostSeine_f$WaterTemp[Seine$WaterTemp == 50.6] <- NA
# Function to fill in missing values with mean
impute.mean <- function(x) replace(x, is.na(x), mean(x, na.rm = TRUE))
# Filling in missing values using impute.mean function from above.
# Variables are renamed because using mutate adds on new columns to the matrix.
# Use impute.mean to fill in NAs, rename updated variables using mutate
Seine_f <- Seine_f %>%
group_by(WYType) %>%
mutate(
Cond = impute.mean(Conductivity),
WTemp = impute.mean(WaterTemp),
SecDepth = impute.mean(Secchi),
Turb = impute.mean(Turbidity),
DOx = impute.mean(DO)) %>%
ungroup()Data Analysis (Seine data)
- Filter for species or sets of species
list_nmds <- c("Sacramento Pikeminnow", "Splittail", "Hitch", "Hardhead", "Sacramento Sucker", "Sacramento Blackfish",
"Wakasagi", "Inland Silverside", "Delta Smelt",
"Carp", "Goldfish", "Hardhead", "Golden Shiner", "Fathead Minnow", "Hitch",
"Rainwater Killifish", "Western Mosquitofish", "Black Crappie", "White Crappie", "Bluegill", "Bigscale Logperch",
"Largemouth Bass", "Smallmouth Bass", "Striped Bass", "Spotted Bass",
"Threadfin Shad", "American Shad")
list_nmds_small <- c("Sacramento Pikeminnow", "Splittail", "Hitch", "Hardhead", "Sacramento Sucker", "Sacramento Blackfish",
"Wakasagi", "Inland Silverside", "Delta Smelt", "Longfin Smelt",
"Largemouth Bass", "Smallmouth Bass", "Striped Bass", "Spotted Bass",
"Threadfin Shad", "American Shad", "Bluegill", "Black Crappie", "Bigscale Logperch")
Seine_tf <- Seine_f %>% filter(CommonName == "Threadfin Shad")
Seine_sucker <- Seine_f %>% filter(CommonName == "Sacramento Sucker")
Seine_lmb <- Seine_f %>% filter(CommonName == "Largemouth Bass")
Seine_black <- Seine_f %>% filter(CommonName == "Sacramento Blackfish")
Seine_pike <- Seine_f %>% filter(CommonName == "Sacramento Pikeminnow")
Seine_natives <- Seine_f %>%filter(CommonName %in% list_native)
Seine_nmds_larger <- Seine_f%>% filter(CommonName %in%list_nmds)
Seine_nmds_0 <- Seine_f %>% filter(CommonName %in% list_nmds_small)Univariate Analyses
Parametric Analyses
T-test
*Data must (approximatley) fit a known statistical model
*Highly used and have a long history
*Measures the difference in population means
- Independent sample t-test (two sample t-test or students t-test)
- determines whether there is a statistically significant difference between the means in two unrelated groups
- example: Whether first year graduate salaries differed based on gender
- Paired t-test
- compares two population means where you have two samples in which observations in one sample can be paired with observations in the other sample.
- example: Before and after measurments on the same subjects
- One-sample t-test
- used to determine whether a sample comes from a population with a specific mean
- example: You sample 1000 doctors and see if their hours differ from 100 hours.
### 1. Independent-samples t-test: Is there a difference in LMB CPUE by survey? ----------------
(lmb.ttest <- t.test(Seine_lmb$CPUE~Seine_lmb$Survey)) # not significant##
## Welch Two Sample t-test
##
## data: Seine_lmb$CPUE by Seine_lmb$Survey
## t = 0.97697, df = 1362.2, p-value = 0.3288
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.002880479 0.008596023
## sample estimates:
## mean in group DJFMP mean in group Yolo
## 0.01439474 0.01153696# Plot
ggplot(Seine_lmb, aes(x = Survey, y = CPUE)) + geom_boxplot()
ggplot(Seine_lmb, aes(x = CPUE, color = Survey)) + geom_density()
ggplot(Seine_lmb, aes(x = Survey, y = CPUE)) + geom_col() # This works best for data with lots of zeros
### 2. Paired t-test: Does a treatment cause a difference? Did Action Phase alter CPUE of LMB? -------------
Seine_lmb2 <- filter(Seine_lmb, ActionPhase!="During")
(lmb.ttest2 <- t.test(Seine_lmb2$CPUE ~ Seine_lmb2$ActionPhase)) # significant##
## Welch Two Sample t-test
##
## data: Seine_lmb2$CPUE by Seine_lmb2$ActionPhase
## t = 2.0514, df = 542.51, p-value = 0.04071
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.0004562724 0.0210537512
## sample estimates:
## mean in group Pre mean in group Post
## 0.019175050 0.008420039# Plot: Figure out the direction of the trend
ggplot(Seine_lmb2, aes(x = ActionPhase, y = CPUE)) + geom_boxplot()
ggplot(Seine_lmb2, aes(x = CPUE, color = ActionPhase)) + geom_density()
ggplot(Seine_lmb2, aes(x = ActionPhase, y = CPUE)) + geom_col() # This works best for data with lots of zeros
### 3. One-sample t-test: Is the CPUE greater than 0? ---------------------------------------
(lmb.ttest3 <- t.test(Seine_lmb$CPUE, mu = 0)) # p < 0.05, Yes, it is##
## One Sample t-test
##
## data: Seine_lmb$CPUE
## t = 6.9746, df = 1653, p-value = 4.42e-12
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## 0.009708318 0.017304984
## sample estimates:
## mean of x
## 0.01350665ANOVA
Run ANOVA
- One-way
- used to determine whether there are any statistically significant differences between the means of two or more independent (unrelated) groups (although you tend to only see it used when there are a minimum of three).
- Two-way
- used to compare the mean differences between groups that have been split on two independent variables (called factors). The primary purpose of a two-way ANOVA is to understand if there is an interaction between the two independent variables on the dependent variable.
### 1. One-way ANOVA: Effect of action phase on Threadfin Shad CPUE
(tf.aov1 <- aov(CPUE~ActionPhase, data = Seine_tf))## Call:
## aov(formula = CPUE ~ ActionPhase, data = Seine_tf)
##
## Terms:
## ActionPhase Residuals
## Sum of Squares 2.4957 329.6404
## Deg. of Freedom 2 1651
##
## Residual standard error: 0.4468345
## Estimated effects may be unbalancedsummary(tf.aov1)## Df Sum Sq Mean Sq F value Pr(>F)
## ActionPhase 2 2.5 1.2478 6.25 0.00198 **
## Residuals 1651 329.6 0.1997
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1### 2. Two-way ANOVA: Effect of action phase and water year type on Threadfin Shad CPUE
(tf.aov2 <- aov(CPUE~ActionPhase + Region, data = Seine_tf))## Call:
## aov(formula = CPUE ~ ActionPhase + Region, data = Seine_tf)
##
## Terms:
## ActionPhase Region Residuals
## Sum of Squares 2.4957 5.3135 324.3269
## Deg. of Freedom 2 3 1648
##
## Residual standard error: 0.4436218
## Estimated effects may be unbalancedsummary(tf.aov2)## Df Sum Sq Mean Sq F value Pr(>F)
## ActionPhase 2 2.5 1.2478 6.341 0.00181 **
## Region 3 5.3 1.7712 9.000 6.52e-06 ***
## Residuals 1648 324.3 0.1968
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1### If both significant, check interaction.
(tf.aov3 <- aov(CPUE~ActionPhase + Region, data = Seine_tf))## Call:
## aov(formula = CPUE ~ ActionPhase + Region, data = Seine_tf)
##
## Terms:
## ActionPhase Region Residuals
## Sum of Squares 2.4957 5.3135 324.3269
## Deg. of Freedom 2 3 1648
##
## Residual standard error: 0.4436218
## Estimated effects may be unbalancedsummary(tf.aov3)## Df Sum Sq Mean Sq F value Pr(>F)
## ActionPhase 2 2.5 1.2478 6.341 0.00181 **
## Region 3 5.3 1.7712 9.000 6.52e-06 ***
## Residuals 1648 324.3 0.1968
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Test Assumptions
- Plot results, can use statistical tests to check if desired but pretty sensitive.
- Residuals are normally distributed
- Residuals are homogeneous across groups
library(car)
# Test for normality of residuals
par(mfrow = c(1,1))
plot(tf.aov2,2)
tf.resid <- residuals(object = tf.aov2)
shapiro.test(tf.resid) # p < 0.05 means not normal##
## Shapiro-Wilk normality test
##
## data: tf.resid
## W = 0.38605, p-value < 2.2e-16# Test for homogeneity of variance.
# If data are normal: Bartlett's test
# If data are nonnnormal or Fligner-Killeen Test: Levene's test (In this case, use this one)
plot(tf.aov2, 1)
bartlett.test(CPUE~interaction(ActionPhase,Region), data = Seine_tf) #p<0.05 means they are NOT homogeneous##
## Bartlett test of homogeneity of variances
##
## data: CPUE by interaction(ActionPhase, Region)
## Bartlett's K-squared = 776.73, df = 11, p-value < 2.2e-16leveneTest(CPUE~ActionPhase*Region, data = Seine_tf) #p<0.05 means they are NOT homogeneous## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 11 4.6714 4.613e-07 ***
## 1642
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Post-Hoc Tests
P-Value Corrections: * Tukey: set family error rate * Bonferroni: divide p-value by number of comparisons * Holm-Bonferroni : sequential bonferroni, more powerful than bonferroni
library(lsmeans)
library(multcomp)
library(multcompView)
leastsquare.tf = lsmeans(tf.aov2,
~ActionPhase|Region,
adjust = "holm")
# Compact letter display - test each comparison
(CLD <- cld(leastsquare.tf, alpha = 0.05, Letters = letters, adjust = "holm"))## Region = CacheSloughComplex:
## ActionPhase lsmean SE df lower.CL upper.CL .group
## Post -0.00621 0.0260 1648 -0.0686 0.0562 a
## Pre 0.05046 0.0251 1648 -0.0097 0.1106 ab
## During 0.09917 0.0232 1648 0.0436 0.1547 b
##
## Region = CentralYolo:
## ActionPhase lsmean SE df lower.CL upper.CL .group
## Post 0.12596 0.0239 1648 0.0687 0.1832 a
## Pre 0.18263 0.0255 1648 0.1216 0.2436 ab
## During 0.23134 0.0240 1648 0.1739 0.2887 b
##
## Region = LowerSacRiver:
## ActionPhase lsmean SE df lower.CL upper.CL .group
## Post 0.10833 0.0328 1648 0.0296 0.1870 a
## Pre 0.16501 0.0326 1648 0.0870 0.2430 ab
## During 0.21372 0.0312 1648 0.1389 0.2886 b
##
## Region = LowerYolo:
## ActionPhase lsmean SE df lower.CL upper.CL .group
## Post 0.09384 0.0297 1648 0.0226 0.1651 a
## Pre 0.15052 0.0303 1648 0.0780 0.2230 ab
## During 0.19923 0.0285 1648 0.1309 0.2676 b
##
## Confidence level used: 0.95
## Conf-level adjustment: bonferroni method for 3 estimates
## P value adjustment: holm method for 3 tests
## significance level used: alpha = 0.05Plot Results
library(FSA)
# One plot idea
pd = position_dodge(0.4) ### How much to jitter the points on the plot
ggplot(CLD,
aes(x = Region,
y = lsmean,
color = ActionPhase,
label = .group)) +
geom_point(shape = 15,
size = 4,
position = pd) +
geom_errorbar(aes(ymin = lower.CL,
ymax = upper.CL),
width = 0.2,
size = 0.7,
position = pd) +
theme_bw() +
theme(axis.title = element_text(face = "bold"),
axis.text = element_text(face = "bold"),
plot.caption = element_text(hjust = 0)) +
ylab("Mean CPUE") +
ggtitle ("Mean Threadfin Shad CPUE",
subtitle = "By Region and Action Phase") +
labs(caption = paste0("\nInterpretation ",
"here \n"),
hjust=0.5) +
geom_text(nudge_x = c(0.1, -0.1, 0.1, -0.1, 0.1, -0.1, -0.1, 0.1),
nudge_y = c(0.1, 0.05, 0.05, 0.05, 0.05 , 0.05, 0.05, 0.05),
color = "black") +
scale_color_manual(values = c("blue", "red", "green"))
# Graphics
# Using standard error
# Need to manually insert the lsmeans significant groupings
Sum.tf = Summarize(CPUE~ActionPhase + Region, data = Seine_tf, digits = 3)
Sum.tf$se = Sum.tf$sd/sqrt(Sum.tf$n)
Sum.tf$se = signif(Sum.tf$se, digits = 3)
#levels(Sum.tf$Season) <- c("Dry 2015", "Wet", "Dry 2016")
ggplot(Sum.tf, aes(x = Region, y = mean, color = ActionPhase)) +
geom_errorbar(aes(ymin = mean-se,
ymax = mean +se),
width = 0.2, size = 0.7, position = position_dodge(0.2)) +
geom_point(aes(shape = ActionPhase), size = 4, position = position_dodge(0.2)) +
# annotate("text", x = 1, y = 5.5, label = "e", size = 6) +
# annotate("text", x = 1.15, y = 3.8, label = "de", size = 6) +
# annotate("text", x = 1.1, y = 2.5, label = "bcd", size = 6) +
# annotate("text", x = 1.85, y = 0.6, label = "ab", size = 6) +
# annotate("text", x = 2, y = 1, label = "ab", size = 6) +
# annotate("text", x = 2.2, y = 0.65, label = "abc", size = 6) +
# annotate("text", x = 2.9, y = 0.45, label = "a", size = 6) +
# annotate("text", x = 3.05, y = 0.4,label = "ab", size=6) +
# annotate("text", x = 3.2, y = 4, label = "cde", size = 6) +
labs(y = expression(paste("Mean CPUE (ind ", m^{-3},")")))+
theme_bw() +
theme(axis.title = element_text(face = "bold"),
axis.text = element_text(size = 14),
legend.text = element_text(size = 13)) +
scale_colour_manual(values = c("#1db918", "#2e8fad", "#e52078"))
ANCOVA
*ANCOVA is a blend of analysis of variance (ANOVA) and regression. It is similar to factorial ANOVA, in that it can tell you what additional information you can get by considering one independent variable (factor) at a time, without the influence of the others.
Non-parametric Analyses
Kruskal-Wallis: only for one factor
library(lattice)
# Check distributions are similar
histogram(~CPUE | ActionPhase,
data = Seine_tf,
layout = c(1,3))
boxplot(CPUE~ActionPhase,
data = Seine_tf,
ylab = "ActionPhase",
xlab = "CPUE")
kruskal.test(CPUE~ActionPhase, data = Seine_tf)##
## Kruskal-Wallis rank sum test
##
## data: CPUE by ActionPhase
## Kruskal-Wallis chi-squared = 18.372, df = 2, p-value = 0.0001025Post-hoc for Kruskal-Wallis * Dunn Test: Appropriate for groups with unequal numbers of observations (Zar 2010) * Nemenyi test: Not appropriate for groups with unequal numbers of observations (Zar 2010) * Pairwise Mann-Whitney U
library(FSA)
library(rcompanion)## Warning: package 'rcompanion' was built under R version 3.6.3### Dunn
(tf.dunn <- dunnTest(CPUE~ActionPhase,
data = Seine_tf,
method = "holm"))## Dunn (1964) Kruskal-Wallis multiple comparison## p-values adjusted with the Holm method.## Comparison Z P.unadj P.adj
## 1 During - Post 4.151433 3.303995e-05 9.911985e-05
## 2 During - Pre 2.796070 5.172820e-03 1.034564e-02
## 3 Post - Pre -1.244619 2.132718e-01 2.132718e-01# Get the letters wit compact letter display
tf.res <- tf.dunn$res
cldList(comparison = tf.res$Comparison,
p.value = tf.res$P.adj,
threshold = 0.05)## Group Letter MonoLetter
## 1 During a a
## 2 Post b b
## 3 Pre b bKolmogorov-Smirnov Test
- Are two distributions different from each other?
- Lower D statistic = more probable that samples came from same distribution. If D >1, more likely they are not from the same distribution
- Can follow up to ask if one is larger than the other
- Example: Compare size distributions from Male vs. Female fish
- Here: Compare CPUE distributions from Threadfin Shad vs. Inland Silverside
# ECDF and K-S TEST
TF <- filter(Seine_f, CommonName=="Threadfin Shad")
ISS <- filter(Seine_f, CommonName == "Inland Silverside")
ks.test(TF$CPUE, ISS$CPUE)##
## Two-sample Kolmogorov-Smirnov test
##
## data: TF$CPUE and ISS$CPUE
## D = 0.47582, p-value < 2.2e-16
## alternative hypothesis: two-sided# Plot cumulative distribution
# Plot data (CPUE) from least to greatest.
Seine_ecdf <- filter(Seine_f, CommonName %in% c("Threadfin Shad", "Inland Silverside"))
ggplot(Seine_ecdf, aes(CPUE, color=CommonName)) +
stat_ecdf() +
labs(x= "CPUE",
y = "Cumulative Probability",
title = "ISS and Threadfin Shad") +
theme_bw() +
annotate("text", x=100, y=0.7, label="D = 0.47582", size=6) +
annotate("text", x =100, y = 0.625, label = "p < 0.05", size = 5)
Goodness of Fit
Chi Square
- How does the observed value differ from expected value?
General Linear Model Code
- Check out data - what kind of distribution does this look like?
- If there are a lot of zeros, you might want to look at zero-inflated possion or negative binomial
- Scale and center continuous variables if very different
- Run full model (all variables)
- Run alternate models, or run dredge to run all possible model combinations
- Use AIC to pick best model
- Check model
library(MuMIn)## Warning: package 'MuMIn' was built under R version 3.6.3library(pscl)## Warning: package 'pscl' was built under R version 3.6.3## Classes and Methods for R developed in the
## Political Science Computational Laboratory
## Department of Political Science
## Stanford University
## Simon Jackman
## hurdle and zeroinfl functions by Achim Zeileislibrary(AER)## Warning: package 'AER' was built under R version 3.6.3## Loading required package: lmtest## Warning: package 'lmtest' was built under R version 3.6.3## Loading required package: zoo## Warning: package 'zoo' was built under R version 3.6.3##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: sandwich## Warning: package 'sandwich' was built under R version 3.6.3# Look at distribution of data - is it zero-inflated?
ggplot(Seine_tf, aes(CPUE)) + geom_histogram(binwidth = 0.1) + theme_bw()
plot_ly(data = Seine_tf, x = ~Survey, y = ~CPUE, type = 'box')# Scale and center continuous variables if needed
Seine_tf_scale <- Seine_tf %>%
mutate(Turb2 = scale(Turb, center = TRUE),
Cond2 = scale(Cond, center = TRUE),
WTemp2 = scale(WTemp),
DOx2 = scale(DOx))
# For CPUE, use offset to account for sampling effort
Seine_tf_scale$Samp <- log(Seine_tf_scale$VolumeSampled)
# Start with normal poisson
L0 <- glm(sum.count ~ Region + ActionPhase + WYType + Survey + Turb2 + Cond2 + WTemp2 + DOx2 +
offset(Samp), family = poisson, data = Seine_tf_scale)
TF.back <- step(L0, direction = "backward")## Start: AIC=41271.96
## sum.count ~ Region + ActionPhase + WYType + Survey + Turb2 +
## Cond2 + WTemp2 + DOx2 + offset(Samp)
##
## Df Deviance AIC
## <none> 38657 41272
## - ActionPhase 2 39051 41662
## - Turb2 1 39061 41673
## - Survey 1 39074 41687
## - DOx2 1 39471 42083
## - WYType 3 39864 42472
## - Region 3 40411 43020
## - WTemp2 1 40442 43055
## - Cond2 1 40597 43210summary(TF.back)##
## Call:
## glm(formula = sum.count ~ Region + ActionPhase + WYType + Survey +
## Turb2 + Cond2 + WTemp2 + DOx2 + offset(Samp), family = poisson,
## data = Seine_tf_scale)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -15.692 -3.175 -1.983 -1.109 37.795
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.416158 0.032489 -105.147 <2e-16 ***
## RegionCentralYolo 1.139674 0.029577 38.533 <2e-16 ***
## RegionLowerSacRiver 0.893184 0.039886 22.394 <2e-16 ***
## RegionLowerYolo 0.734504 0.031858 23.055 <2e-16 ***
## ActionPhaseDuring 0.330513 0.019436 17.005 <2e-16 ***
## ActionPhasePost -0.032401 0.026298 -1.232 0.218
## WYTypeC -0.343248 0.028815 -11.912 <2e-16 ***
## WYTypeD -0.379042 0.032456 -11.679 <2e-16 ***
## WYTypeW 0.353282 0.019860 17.789 <2e-16 ***
## SurveyYolo 0.478734 0.023978 19.965 <2e-16 ***
## Turb2 0.141655 0.006244 22.687 <2e-16 ***
## Cond2 0.346987 0.006445 53.841 <2e-16 ***
## WTemp2 0.389507 0.007605 51.218 <2e-16 ***
## DOx2 0.224957 0.007746 29.043 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 50134 on 1653 degrees of freedom
## Residual deviance: 38657 on 1640 degrees of freedom
## AIC: 41272
##
## Number of Fisher Scoring iterations: 7par(mfrow = c(2,2))
plot(TF.back)
# Check for overdispersion. Overdispersed if >1: Use NB
dispersiontest(TF.back, trafo = 1)##
## Overdispersion test
##
## data: TF.back
## z = 4.529, p-value = 2.963e-06
## alternative hypothesis: true alpha is greater than 0
## sample estimates:
## alpha
## 68.37969### Model: zero-inflated poisson -------------------------------
# You can only have full count data, not CPUE.
# Need to add the offset!
f1 <- formula(sum.count ~ Region + ActionPhase + WYType + Survey +
Turb2 + Cond2 + WTemp2 + DOx2 + offset(Samp))
zip1 <- zeroinfl(f1, dist = "poisson", link = "logit", data = Seine_tf_scale); summary(zip1)##
## Call:
## zeroinfl(formula = f1, data = Seine_tf_scale, dist = "poisson", link = "logit")
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## -10.8393 -0.6789 -0.4068 -0.2389 90.2956
##
## Count model coefficients (poisson with log link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.001944 0.034460 -58.096 < 2e-16 ***
## RegionCentralYolo 1.422792 0.031522 45.137 < 2e-16 ***
## RegionLowerSacRiver 1.151508 0.043151 26.685 < 2e-16 ***
## RegionLowerYolo 0.967594 0.033533 28.855 < 2e-16 ***
## ActionPhaseDuring 0.152665 0.020211 7.553 4.24e-14 ***
## ActionPhasePost -0.211540 0.030858 -6.855 7.12e-12 ***
## WYTypeC -0.332060 0.029205 -11.370 < 2e-16 ***
## WYTypeD -0.568581 0.032777 -17.347 < 2e-16 ***
## WYTypeW 0.098849 0.020282 4.874 1.09e-06 ***
## SurveyYolo -0.679347 0.025096 -27.070 < 2e-16 ***
## Turb2 0.122576 0.009340 13.124 < 2e-16 ***
## Cond2 0.243778 0.006649 36.664 < 2e-16 ***
## WTemp2 0.333656 0.011298 29.531 < 2e-16 ***
## DOx2 0.244617 0.008503 28.770 < 2e-16 ***
##
## Zero-inflation model coefficients (binomial with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.87377 0.20243 -9.256 < 2e-16 ***
## RegionCentralYolo -0.10339 0.19509 -0.530 0.596120
## RegionLowerSacRiver 0.42717 0.23509 1.817 0.069209 .
## RegionLowerYolo 0.22528 0.22667 0.994 0.320274
## ActionPhaseDuring -0.59641 0.16439 -3.628 0.000286 ***
## ActionPhasePost -0.56218 0.22875 -2.458 0.013988 *
## WYTypeC 0.05927 0.19173 0.309 0.757210
## WYTypeD -0.23081 0.24653 -0.936 0.349150
## WYTypeW -0.76708 0.16676 -4.600 4.23e-06 ***
## SurveyYolo -3.14038 0.18631 -16.855 < 2e-16 ***
## Turb2 -0.49948 0.08989 -5.557 2.75e-08 ***
## Cond2 -0.13145 0.06227 -2.111 0.034774 *
## WTemp2 -0.43138 0.09326 -4.626 3.74e-06 ***
## DOx2 0.13556 0.07280 1.862 0.062597 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Number of iterations in BFGS optimization: 33
## Log-likelihood: -1.385e+04 on 28 Df### Model: zero-inflated negative binomial -------------------------------------
zinb1 <- zeroinfl(f1, na.action = "na.fail", dist="negbin", link = "logit", data = Seine_tf_scale);summary(zinb1)##
## Call:
## zeroinfl(formula = f1, data = Seine_tf_scale, na.action = "na.fail",
## dist = "negbin", link = "logit")
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## -0.5840 -0.4136 -0.2359 -0.1020 44.8409
##
## Count model coefficients (negbin with log link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.62884 0.23659 -11.111 < 2e-16 ***
## RegionCentralYolo 1.97135 0.23190 8.501 < 2e-16 ***
## RegionLowerSacRiver 1.09760 0.35102 3.127 0.001767 **
## RegionLowerYolo 1.34225 0.24399 5.501 3.77e-08 ***
## ActionPhaseDuring 0.56227 0.16805 3.346 0.000821 ***
## ActionPhasePost -0.18972 0.21401 -0.886 0.375371
## WYTypeC 0.15510 0.18335 0.846 0.397603
## WYTypeD -0.77634 0.24079 -3.224 0.001264 **
## WYTypeW 0.06992 0.15780 0.443 0.657716
## SurveyYolo -0.90083 0.19718 -4.568 4.91e-06 ***
## Turb2 0.07749 0.05788 1.339 0.180613
## Cond2 0.28758 0.11655 2.467 0.013607 *
## WTemp2 0.55053 0.08920 6.172 6.76e-10 ***
## DOx2 0.40450 0.08701 4.649 3.34e-06 ***
## Log(theta) -1.07104 0.06002 -17.844 < 2e-16 ***
##
## Zero-inflation model coefficients (binomial with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.07706 0.43776 -7.029 2.08e-12 ***
## RegionCentralYolo -0.15714 0.37221 -0.422 0.67289
## RegionLowerSacRiver -0.06357 0.39943 -0.159 0.87356
## RegionLowerYolo 0.27803 0.52446 0.530 0.59602
## ActionPhaseDuring -0.86203 0.30955 -2.785 0.00536 **
## ActionPhasePost -2.68552 0.48653 -5.520 3.40e-08 ***
## WYTypeC -0.06660 0.36540 -0.182 0.85536
## WYTypeD -0.62095 0.47342 -1.312 0.18965
## WYTypeW 0.31395 0.36392 0.863 0.38831
## SurveyYolo -5.86023 1.39824 -4.191 2.78e-05 ***
## Turb2 -3.46293 0.41888 -8.267 < 2e-16 ***
## Cond2 -0.18549 0.13541 -1.370 0.17072
## WTemp2 -0.64932 0.23542 -2.758 0.00581 **
## DOx2 0.84448 0.17597 4.799 1.59e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Theta = 0.3427
## Number of iterations in BFGS optimization: 43
## Log-likelihood: -3237 on 29 Df### Dredge function runs all the available models to tell you what the best model is.
# AIC within 2 = about the same model
# Pick what makes sense for your system, or average your top models
# Use AIC to pick the best models, then look at variables that aren't significant, and re-run model without significant variables
# m1.dredge <- dredge(zinb1)
# Take out survey (not significant)
f2 <- formula(sum.count ~ Region + ActionPhase + WYType + Turb2 + Cond2 + WTemp2 + DOx2)
zinb2 <- zeroinfl(f2, na.action = "na.fail", dist="negbin", link = "logit", data = Seine_tf_scale) ; summary(zinb2)##
## Call:
## zeroinfl(formula = f2, data = Seine_tf_scale, na.action = "na.fail",
## dist = "negbin", link = "logit")
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## -0.55796 -0.42419 -0.19052 -0.07899 142.94954
##
## Count model coefficients (negbin with log link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.35650 0.22904 5.922 3.17e-09 ***
## RegionCentralYolo 1.71465 0.20156 8.507 < 2e-16 ***
## RegionLowerSacRiver 1.02258 0.28378 3.603 0.000314 ***
## RegionLowerYolo 0.89870 0.19020 4.725 2.30e-06 ***
## ActionPhaseDuring 0.54012 0.17069 3.164 0.001555 **
## ActionPhasePost -0.12232 0.21834 -0.560 0.575331
## WYTypeC -0.13793 0.18066 -0.763 0.445169
## WYTypeD -0.73700 0.23984 -3.073 0.002120 **
## WYTypeW 0.18007 0.15517 1.160 0.245864
## Turb2 0.04757 0.05738 0.829 0.407131
## Cond2 0.10714 0.06102 1.756 0.079116 .
## WTemp2 0.52062 0.08650 6.019 1.76e-09 ***
## DOx2 0.35866 0.08936 4.013 5.98e-05 ***
## Log(theta) -1.16228 0.05565 -20.887 < 2e-16 ***
##
## Zero-inflation model coefficients (binomial with logit link):
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -8.24798 1.42708 -5.780 7.49e-09 ***
## RegionCentralYolo 0.18055 0.41380 0.436 0.66260
## RegionLowerSacRiver 0.35358 0.44042 0.803 0.42207
## RegionLowerYolo -1.01985 0.39302 -2.595 0.00946 **
## ActionPhaseDuring 0.31230 0.34216 0.913 0.36139
## ActionPhasePost -0.91380 0.43004 -2.125 0.03359 *
## WYTypeC 1.27898 0.46025 2.779 0.00545 **
## WYTypeD -0.06631 0.52887 -0.125 0.90022
## WYTypeW -0.20728 0.37953 -0.546 0.58497
## Turb2 -2.49070 0.42585 -5.849 4.95e-09 ***
## Cond2 -27.17737 4.07591 -6.668 2.60e-11 ***
## WTemp2 -0.01475 0.16854 -0.087 0.93028
## DOx2 -0.13506 0.18753 -0.720 0.47140
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Theta = 0.3128
## Number of iterations in BFGS optimization: 50
## Log-likelihood: -3197 on 27 Dfm2.dredge <- dredge(zinb2)## Fixed terms are "count_(Intercept)" and "zero_(Intercept)"## Warning in value[[3L]](cond): system is computationally singular: reciprocal
## condition number = 2.56432e-33FALSE# Diagnostic Plots -------------------------------------
# Model Validation
# Calculate residuals
EP1 <- resid(zinb2, type = "pearson")
# Diagnostic Plots
par(mfrow = c(2,5))
plot(x=zinb2$fitted.values, y = EP1, main = "Pearson residuals")
qqnorm(EP1)
plot(x=Seine_tf_scale$ActionPhase,y = EP1, main = "Action Phase")
plot(x=Seine_tf_scale$WYType, EP1, main = "Water Year Type")
plot(x=Seine_tf_scale$Region, EP1, main = "Water Year Type")
plot(x=Seine_tf_scale$Cond2, EP1, main = "Conductivity")
plot(x=Seine_tf_scale$WTemp2, EP1, main = "Water Temperature")
plot(x=Seine_tf_scale$Turb2, EP1, main = "Turbidity")
plot(x=Seine_tf_scale$DOx2, EP1, main = "DO")
Multivariate Analyses
Preparation
Some summary stats
Look for outliers in species data
Look at initial trends - env. vs. species
Pick transformations needed
Summary Stats
snstatsall <- Seine_nmds_larger%>%
group_by(CommonName) %>%
summarize(mean = mean(CPUE),
max = max(CPUE),
min = min(CPUE),
sum = sum(CPUE),
CV = sd(CPUE)/mean,
zeros = sum(CPUE == 0),
n = n(),
prop.absent = round(zeros/n,2))
snstats <- Seine_nmds_0 %>%
group_by(CommonName) %>%
summarize(mean = mean(CPUE),
max = max(CPUE),
min = min(CPUE),
sum = sum(CPUE),
CV = sd(CPUE)/mean,
zeros = sum(CPUE == 0),
n = n(),
prop.absent = round(zeros/n,2))- Remove certain species
- Need to make decisions about which species to keep in
- Species occurring in fewer than 5% samples
- Species occurring in >95% samples
- Species with CV (standard deviation/mean) < 10%
Here: * Remove species that are not present: Hardhead, Smallmouth Bass, Longfin Smelt * Species < 5% of samples: Hitch, Wakasagi, Delta Smelt, Sacramento Blackfish
notabund <- c("Hardhead", "Smallmouth Bass", "Longfin Smelt", "Hitch", "Wakasagi", "Delta Smelt", "Sacramento Blackfish")
Seine_nmds <- filter(Seine_nmds_0, !(CommonName %in% notabund))Exploration/QC
- Look for outliers in species data
- Click species to remove, look at each individual species for any obvious outliers
# Overall CPUE
par(mfrow = c(1,1))
index= seq(1,length(Seine_nmds$CPUE))
# Explore each species - look for outliers here by adding and removing species
Seine_nmds%>%
plot_ly() %>%
add_trace(x = ~index,
y = ~CPUE,
color = ~CommonName,
colors = "Set3",
type = "scatter")- Look at initial trends - environment vs. species
# Threadfin vs environmental
threadfin1 <- ggplot(Seine_tf, aes(x = WTemp, y = CPUE)) + geom_point() + theme_bw()
threadfin2 <- ggplot(Seine_tf, aes(x = Cond, y = CPUE)) + geom_point() + theme_bw()
threadfin3 <- ggplot(Seine_tf, aes(x = Turb, y = CPUE)) + geom_point() + theme_bw()
threadfin4 <- ggplot(Seine_tf, aes(x = DOx, y = CPUE)) + geom_point() + theme_bw()
grid.arrange(threadfin1, threadfin2, threadfin3, threadfin4, top = "Threadfin CPUE by Environmental Variable")
# Sac Sucker vs environmental
sucker1 <- ggplot(Seine_sucker, aes(x = WTemp, y = CPUE)) + geom_point() + theme_bw()
sucker2 <- ggplot(Seine_sucker, aes(x = Cond, y = CPUE)) + geom_point() + theme_bw()
sucker3 <- ggplot(Seine_sucker, aes(x = Turb, y = CPUE)) + geom_point() + theme_bw()
sucker4 <- ggplot(Seine_sucker, aes(x = DOx, y = CPUE)) + geom_point() + theme_bw()
grid.arrange(sucker1, sucker2, sucker3,sucker4, top = "Sac Sucker CPUE by Environmental Variable")
# Largemouth Bass vs environmental
lmb1 <- ggplot(Seine_lmb, aes(x = WTemp, y = CPUE)) + geom_point() + theme_bw()
lmb2 <- ggplot(Seine_lmb, aes(x = Cond, y = CPUE)) + geom_point() + theme_bw()
lmb3 <- ggplot(Seine_lmb, aes(x = Turb, y = CPUE)) + geom_point() + theme_bw()
lmb4 <- ggplot(Seine_lmb, aes(x = DOx, y = CPUE)) + geom_point() + theme_bw()
grid.arrange(lmb1, lmb2, lmb3, lmb4, top = "Largemouth Bass CPUE by Environmental Variable")
Transformations
- For highly skewed variables, and to help you meet assumptions of a statistical test
- Can help emphasize presence/absence
- Equalize relative importance of variabilities
- Pick transformations that do not change the rank - power, log, arcsine, arcsine sqrt
- Log of sqrt for highly skewed data, or ranging >2 order magnitude
- Arcsine sqrt for proportional data
- Use same transformation for same variable set (e.g. species)
- Consider binary transformation when percent of zero values is high (>50%) or distinct values low (<10)
# Environmental Matrix
Seine_pca <- sample_n(Seine_nmds, 300)
Seine_env <- Seine_pca %>% dplyr::select(c(26:30))
# Check for normality of variables
cond <- Seine_env$Cond
temp <- Seine_env$WTemp
sd <- Seine_env$SecDepth
turb <- Seine_env$Turb
do <- Seine_env$DOx
hist(cond)
hist(log(cond+1)) # Use this
qqnorm(log(cond+1))
hist(temp)
hist(log(temp+1)) # Use this
hist(sqrt(temp))
qqnorm(temp)
qqnorm(log(temp+1))
hist(sd) # Keep it?
hist(log(sd+1))
qqnorm(sd)
qqnorm(log(sd+1))
hist(turb)
hist(sqrt(turb))
hist(log(turb+1))
qqnorm(log(turb+1)) # Use this
hist(do) # Keep it
qqnorm(do)
PCA
Run PCA
- Apply transformations
- If you have variables with different units/scales, choose the correlation matrix (scale = TRUE). Then you do not need to scale your data beforehand.
- Run PCA
- Check PCA (Scree plot, Randomization Tests)
source('biostats.R')
library(vegan)
library(ggfortify)
### Transform to get close to normality assumptions
Seine_env_t <- Seine_env %>% mutate(Cond = log(Cond + 1),
WTemp = log(WTemp + 1),
Turb = log(Turb + 1)) %>%
as.data.frame()
row.names(Seine_env_t) <- row.names(Seine_env_t)
### Run PCA. Center and Scale the data (correlation matrix).
pca.env <- prcomp(Seine_env_t, center=T, scale.=T)
summary(pca.env)## Importance of components:
## PC1 PC2 PC3 PC4 PC5
## Standard deviation 1.317 1.1461 0.9140 0.8168 0.67001
## Proportion of Variance 0.347 0.2627 0.1671 0.1334 0.08978
## Cumulative Proportion 0.347 0.6097 0.7768 0.9102 1.00000### Check how well PCA worked
# Scree Plot with Broken Stick values.
# If eigenvalue is greater than broken stick value it is "significant"
screeplot(pca.env, bstick = TRUE) # According to this, don't keep PC1 and PC2
# Monte Carlo Randomization
# This is slow. Ideally, have several dimensions (up to number of variables) to look at trend.
# ordi.monte(Seine_env_t, ord = 'pca', dim = 5) # According to this, keep PC1 and PC2
### Check which variables matter
# Loadings. Generally, if magnitude >/= 0.3 this is important.
pca.env$rotation## PC1 PC2 PC3 PC4 PC5
## Cond 0.6375704 -0.08878988 0.1256680 0.2657685 -0.7065374
## WTemp 0.3131169 -0.52724578 -0.6590205 0.2772202 0.3358729
## SecDepth -0.2411527 -0.57264653 0.6119790 0.4689510 0.1395991
## Turb 0.4193001 0.55067114 0.2139776 0.4545542 0.5182112
## DOx -0.5113655 0.28803732 -0.3599927 0.6526726 -0.3161702# Structure coefficients: linear correlations between original variables and PC scores
pca.structure(pca.env, Seine_env_t, dim = 5, cutoff = 0.4)##
## Structure Correlations:## PC1 PC2 PC3 PC4 PC5
## Cond 0.84 -0.473
## WTemp 0.412 -0.604 -0.602
## SecDepth -0.656 0.559
## Turb 0.552 0.631
## DOx -0.674 0.533Plot
- Plot and interpret PCA
# Autoplot has best customization, looks nice
# use the "data = " to bring in original dataset so we can
# color-code by factors
autoplot(pca.env, data = Seine_pca, colour = 'ActionPhase', loadings = TRUE,
loadings.label = TRUE,
loadings.colour = "black",
loadings.label.vjust = -.5,
loadings.label.col = "black",
loadings.label.size = 4,
loadings.label.font = 4) +
theme_bw()
autoplot(pca.env, data = Seine_pca, colour = 'WYType', loadings = TRUE,
loadings.label = TRUE,
loadings.colour = "black",
loadings.label.vjust = -.5,
loadings.label.col = "black",
loadings.label.size = 4,
loadings.label.font = 4) +
theme_bw()
NMDS
Prep
- Pick your variables
- Switch to wide format (species listed across the top)
- Remove any row where nothing was caught
Matrix
Seine_f_sp <- Seine_nmds %>% dplyr::select(c("Survey", "StationCode", "Date", "FlowPulseType", "WYType",
"ActionPhase", "Region", "Month", "CommonName", "CPUE", "Cond",
"WTemp", "SecDepth", "Turb", "DOx"))
# Species Matrix
Seine_sp_w <- Seine_f_sp %>% pivot_wider(names_from = CommonName, values_from = CPUE, values_fill = list(CPUE=0)) %>% ungroup()
# Remove any row where there is no catch for the day.
Seine_sp_sum <- Seine_sp_w %>% mutate(Total = dplyr::select(., 14:25) %>% rowSums(na.rm = TRUE)) %>%
filter(Total !=0)Transform and/or standardize for nMDS
- Some options for transformations: sqrt, log, absence/presence
# Sqrt transform data
sqrt.seine <- Seine_sp_sum %>% mutate_if(is.numeric, function(x) {
sqrt(x)
})
# Log transform data
log.seine <- Seine_sp_sum %>% mutate_if(is.numeric, function(x) {
log(x + 1) })
# Absence/Presence data
bin.seine <- Seine_sp_sum %>% mutate_if(is.numeric, function(x) {
case_when(x>0 ~0,
x ==0 ~1)})
# Proportional dataRun NMDS
- Run
- Currently a subset of data since otherwise even 2000 iterations won’t converge :(
- Went with sqrt transformation - least change
library(vegan)
test.seine <- sample_n(sqrt.seine, 120)
str(test.seine)
# NMDS Seine
# This can be slow
seine.nmds <- metaMDS(test.seine[,14:25], distance="bray", k=2, trymax=500, autotransform = FALSE)
seine.nmds- Check NMDS #### Interpretation
- Stress < 0.15 is acceptable fit.
- Check stressplot.
# Scree Plot - what should k=?
# This can be slow
nmds.scree(test.seine[,14:25], distance='bray', k=5, trymax = 300, autotransform = FALSE) 
### Check NMDS solution
# Large scatter is not good
stressplot(seine.nmds)
Plots!
- Plot Results.
- Resources:
- https://jonlefcheck.net/2012/10/24/nmds-tutorial-in-r/
- https://rpubs.com/collnell/manova
- https://chrischizinski.github.io/rstats/vegan-ggplot2/
### NMDS scores
seine.scores <- as.data.frame(scores(seine.nmds))
# Need a category to merge scores with the rest of env data
row.names(seine.scores) <- row.names(test.seine)
seine.nmdsplot <- cbind(seine.scores, test.seine)
# Make Plot
plot(seine.nmds)
ordiplot(seine.nmds, type = "n")
orditorp(seine.nmds, display = "species", col = "red", air = 0.01)
orditorp(seine.nmds, display = "sites", cex = 1, air = 0.01)
species.scores <- as.data.frame(scores(seine.nmds, "species"))
species.scores$species <- rownames(species.scores)
head(species.scores)## NMDS1 NMDS2 species
## American Shad 0.10675580 0.1866564 American Shad
## Bigscale Logperch -0.58481110 0.5298449 Bigscale Logperch
## Black Crappie -0.86360660 0.8683071 Black Crappie
## Bluegill -0.76474645 0.3631291 Bluegill
## Inland Silverside -0.02075581 -0.6972043 Inland Silverside
## Largemouth Bass -0.51293357 -0.2759583 Largemouth Bass# Prettier Plots
# Option 1
ggplot(seine.nmdsplot, aes(NMDS1, NMDS2, color = ActionPhase)) +
geom_point(position = position_jitter(.1)) +
geom_text(aes(label = WYType)) +
stat_ellipse(type = 't', size = 1) +
annotate("text", x = min(seine.nmdsplot$NMDS1), y = min(seine.nmdsplot$NMDS2), label = paste('Stress = ', round(seine.nmds$stress,3))) + # Add stress to plot
theme_minimal() 
# Option 2
# With species scores and boxes
# Make the datasets for the boxes
grp.a <- seine.nmdsplot[seine.nmdsplot$ActionPhase == "Pre", ][chull(seine.nmdsplot[seine.nmdsplot$ActionPhase ==
"Pre", c("NMDS1", "NMDS2")]), ] # hull values for grp A
grp.b <- seine.nmdsplot[seine.nmdsplot$ActionPhase == "During", ][chull(seine.nmdsplot[seine.nmdsplot$ActionPhase ==
"During", c("NMDS1", "NMDS2")]), ] # hull values for grp B
grp.c<- seine.nmdsplot[seine.nmdsplot$ActionPhase == "Post", ][chull(seine.nmdsplot[seine.nmdsplot$ActionPhase ==
"Post", c("NMDS1", "NMDS2")]), ] # hull values for grp C
hull.data0 <- rbind(grp.a, grp.b) #combine grp.a and grp.b
hull.data <- rbind(hull.data0,grp.c)
# Plot
ggplot() +
geom_point(data = seine.nmdsplot, aes(x = NMDS1, y = NMDS2, color = ActionPhase),
position = position_jitter(.1)) +
geom_text(data = seine.nmdsplot, aes(NMDS1, NMDS2, label = WYType, color = ActionPhase)) +
geom_text(data = species.scores, aes(x = NMDS1, y = NMDS2, label= species), color = "black", size = 5) +
theme_minimal() +
annotate("text", x = min(seine.nmdsplot$NMDS1), y = min(seine.nmdsplot$NMDS2), label = paste('Stress = ', round(seine.nmds$stress,3))) + # Add stress to plot
geom_polygon(data=hull.data,aes(x=NMDS1,y=NMDS2,fill=ActionPhase,group=ActionPhase),alpha=0.30) 
PERMANOVA
Run Models
- You can include both continuous and categorical variables
- Transform continuous variables
- Standardize species data (basically becomes proportional data) to reduce influence of large numbers. Could also do sqrt transformation.
- Run PERMANOVA with each variable separately. Only keep significant variables.
- Create model that is significant with greatest R2, move down the list until new variables are not signficant.
- For any categorical variables, test interactions as well.
# Row standardization
seine.st <- data.stand(Seine_sp_sum[,14:25], method = 'total', margin = 'row', plot = F)
# Individual permanova models
(perm.WY <- adonis(formula = seine.st~WYType, data = Seine_sp_sum, method = "bray", permutations = 99))##
## Call:
## adonis(formula = seine.st ~ WYType, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## WYType 3 3.09 1.02896 4.6551 0.00862 0.01 **
## Residuals 1606 354.99 0.22104 0.99138
## Total 1609 358.08 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(perm.Action <- adonis(formula = seine.st~ActionPhase, data = Seine_sp_sum, method = "bray", permutations = 99))##
## Call:
## adonis(formula = seine.st ~ ActionPhase, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## ActionPhase 2 2.55 1.27653 5.7701 0.00713 0.01 **
## Residuals 1607 355.52 0.22123 0.99287
## Total 1609 358.08 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(perm.FlowPulse <- adonis(formula = seine.st~FlowPulseType, data = Seine_sp_sum, method = "bray", permutations = 99))##
## Call:
## adonis(formula = seine.st ~ FlowPulseType, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## FlowPulseType 3 2.18 0.72766 3.2836 0.0061 0.01 **
## Residuals 1606 355.89 0.22160 0.9939
## Total 1609 358.08 1.0000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(perm.Month <- adonis(formula = seine.st~Month, data = Seine_sp_sum, method = "bray", permutations = 99))##
## Call:
## adonis(formula = seine.st ~ Month, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Month 5 6.10 1.21925 5.5562 0.01703 0.01 **
## Residuals 1604 351.98 0.21944 0.98297
## Total 1609 358.08 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(perm.Survey <- adonis(formula = seine.st~Region, data = Seine_sp_sum, method = "bray", permutations = 99))##
## Call:
## adonis(formula = seine.st ~ Region, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Region 3 40.70 13.5681 68.659 0.11368 0.01 **
## Residuals 1606 317.37 0.1976 0.88632
## Total 1609 358.08 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1perm.2 <- adonis(formula = seine.st~Region * Month, data = Seine_sp_sum, method = "bray",
permutations = 99)
perm.2##
## Call:
## adonis(formula = seine.st ~ Region * Month, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Region 3 40.70 13.5681 70.177 0.11368 0.01 **
## Month 5 5.49 1.0986 5.682 0.01534 0.01 **
## Region:Month 15 5.24 0.3493 1.807 0.01463 0.01 **
## Residuals 1586 306.64 0.1933 0.85635
## Total 1609 358.08 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Homogeneity of Variance
- Test for Homogeneity of Variance
- Choose variables in your model
- You want the anova not to be significant (significant means variances are not homogeneous)
- Boxplots should be pretty equal
# Make dissimilarity matrix
spe.d <- vegdist(seine.st, "bray")
# StationCode
(sp.bdp <- betadisper(spe.d, Seine_sp_sum$Region))##
## Homogeneity of multivariate dispersions
##
## Call: betadisper(d = spe.d, group = Seine_sp_sum$Region)
##
## No. of Positive Eigenvalues: 294
## No. of Negative Eigenvalues: 787
##
## Average distance to median:
## CacheSloughComplex CentralYolo LowerSacRiver LowerYolo
## 0.2224 0.5223 0.2023 0.3346
##
## Eigenvalues for PCoA axes:
## (Showing 8 of 1081 eigenvalues)
## PCoA1 PCoA2 PCoA3 PCoA4 PCoA5 PCoA6 PCoA7 PCoA8
## 142.59 62.00 34.55 25.24 24.39 22.07 19.02 18.54anova(sp.bdp)## Analysis of Variance Table
##
## Response: Distances
## Df Sum Sq Mean Sq F value Pr(>F)
## Groups 3 29.669 9.8895 123.58 < 2.2e-16 ***
## Residuals 1606 128.519 0.0800
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1permutest(sp.bdp,pairwise=TRUE)##
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 999
##
## Response: Distances
## Df Sum Sq Mean Sq F N.Perm Pr(>F)
## Groups 3 29.669 9.8895 123.58 999 0.001 ***
## Residuals 1606 128.519 0.0800
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
## CacheSloughComplex CentralYolo LowerSacRiver LowerYolo
## CacheSloughComplex 1.0000e-03 4.5000e-01 0.001
## CentralYolo 3.1020e-61 1.0000e-03 0.001
## LowerSacRiver 4.2483e-01 6.3558e-52 0.001
## LowerYolo 4.8538e-07 7.4989e-26 2.4494e-07plot(sp.bdp, ellipse = TRUE)
boxplot(sp.bdp)
# Month
(sp.bdp2 <- betadisper(spe.d, Seine_sp_sum$Month))##
## Homogeneity of multivariate dispersions
##
## Call: betadisper(d = spe.d, group = Seine_sp_sum$Month)
##
## No. of Positive Eigenvalues: 294
## No. of Negative Eigenvalues: 787
##
## Average distance to median:
## 6 7 8 9 10 11
## 0.5940 0.4078 0.3614 0.3455 0.3889 0.3987
##
## Eigenvalues for PCoA axes:
## (Showing 8 of 1081 eigenvalues)
## PCoA1 PCoA2 PCoA3 PCoA4 PCoA5 PCoA6 PCoA7 PCoA8
## 142.59 62.00 34.55 25.24 24.39 22.07 19.02 18.54anova(sp.bdp2)## Analysis of Variance Table
##
## Response: Distances
## Df Sum Sq Mean Sq F value Pr(>F)
## Groups 5 2.006 0.40114 3.3466 0.005187 **
## Residuals 1604 192.263 0.11986
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1permutest(sp.bdp2,pairwise=TRUE)##
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 999
##
## Response: Distances
## Df Sum Sq Mean Sq F N.Perm Pr(>F)
## Groups 5 2.006 0.40114 3.3466 999 0.005 **
## Residuals 1604 192.263 0.11986
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
## 6 7 8 9 10 11
## 6 0.00500000 0.00100000 0.00100000 0.00400000 0.008
## 7 0.00589699 0.16900000 0.09400000 0.59100000 0.837
## 8 0.00030353 0.17233564 0.47400000 0.22200000 0.392
## 9 0.00029747 0.08935643 0.46255086 0.08800000 0.284
## 10 0.00403739 0.61937007 0.22506651 0.08158716 0.852
## 11 0.00767118 0.87018153 0.41620055 0.27964219 0.84799411plot(sp.bdp2, ellipse = TRUE)
boxplot(sp.bdp2)
# WYType
sp.bdp3 <- betadisper(spe.d, Seine_sp_sum$WYType)
sp.bdp3##
## Homogeneity of multivariate dispersions
##
## Call: betadisper(d = spe.d, group = Seine_sp_sum$WYType)
##
## No. of Positive Eigenvalues: 294
## No. of Negative Eigenvalues: 787
##
## Average distance to median:
## BN C D W
## 0.3799 0.3255 0.4120 0.3894
##
## Eigenvalues for PCoA axes:
## (Showing 8 of 1081 eigenvalues)
## PCoA1 PCoA2 PCoA3 PCoA4 PCoA5 PCoA6 PCoA7 PCoA8
## 142.59 62.00 34.55 25.24 24.39 22.07 19.02 18.54anova(sp.bdp3)## Analysis of Variance Table
##
## Response: Distances
## Df Sum Sq Mean Sq F value Pr(>F)
## Groups 3 1.263 0.42085 3.4755 0.01548 *
## Residuals 1606 194.476 0.12109
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1permutest(sp.bdp3,pairwise=TRUE)##
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 999
##
## Response: Distances
## Df Sum Sq Mean Sq F N.Perm Pr(>F)
## Groups 3 1.263 0.42085 3.4755 999 0.019 *
## Residuals 1606 194.476 0.12109
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
## BN C D W
## BN 0.0320000 0.3100000 0.654
## C 0.0306297 0.0110000 0.007
## D 0.3032466 0.0097894 0.423
## W 0.6470484 0.0055393 0.4275720plot(sp.bdp3, ellipse = TRUE)
boxplot(sp.bdp3)
# ActionPhase
sp.bdp4 <- betadisper(spe.d, Seine_sp_sum$ActionPhase)
sp.bdp4##
## Homogeneity of multivariate dispersions
##
## Call: betadisper(d = spe.d, group = Seine_sp_sum$ActionPhase)
##
## No. of Positive Eigenvalues: 294
## No. of Negative Eigenvalues: 787
##
## Average distance to median:
## Pre During Post
## 0.4138 0.3394 0.3814
##
## Eigenvalues for PCoA axes:
## (Showing 8 of 1081 eigenvalues)
## PCoA1 PCoA2 PCoA3 PCoA4 PCoA5 PCoA6 PCoA7 PCoA8
## 142.59 62.00 34.55 25.24 24.39 22.07 19.02 18.54anova(sp.bdp4)## Analysis of Variance Table
##
## Response: Distances
## Df Sum Sq Mean Sq F value Pr(>F)
## Groups 2 1.537 0.76831 6.3302 0.001826 **
## Residuals 1607 195.045 0.12137
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1permutest(sp.bdp4,pairwise=TRUE)##
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 999
##
## Response: Distances
## Df Sum Sq Mean Sq F N.Perm Pr(>F)
## Groups 2 1.537 0.76831 6.3302 999 0.002 **
## Residuals 1607 195.045 0.12137
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
## Pre During Post
## Pre 0.00100000 0.165
## During 0.00030026 0.062
## Post 0.15430722 0.04585440plot(sp.bdp4, ellipse = TRUE)
boxplot(sp.bdp4)
# FlowPulseType
sp.bdp5 <- betadisper(spe.d, Seine_sp_sum$FlowPulseType)
sp.bdp5##
## Homogeneity of multivariate dispersions
##
## Call: betadisper(d = spe.d, group = Seine_sp_sum$FlowPulseType)
##
## No. of Positive Eigenvalues: 294
## No. of Negative Eigenvalues: 787
##
## Average distance to median:
## CA MA-Ag MA-SR NF
## 0.3982 0.3813 0.4100 0.3582
##
## Eigenvalues for PCoA axes:
## (Showing 8 of 1081 eigenvalues)
## PCoA1 PCoA2 PCoA3 PCoA4 PCoA5 PCoA6 PCoA7 PCoA8
## 142.59 62.00 34.55 25.24 24.39 22.07 19.02 18.54anova(sp.bdp5)## Analysis of Variance Table
##
## Response: Distances
## Df Sum Sq Mean Sq F value Pr(>F)
## Groups 3 0.619 0.20647 1.6972 0.1657
## Residuals 1606 195.367 0.12165permutest(sp.bdp5,pairwise=TRUE)##
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 999
##
## Response: Distances
## Df Sum Sq Mean Sq F N.Perm Pr(>F)
## Groups 3 0.619 0.20647 1.6972 999 0.163
## Residuals 1606 195.367 0.12165
##
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
## CA MA-Ag MA-SR NF
## CA 0.54900 0.72000 0.062
## MA-Ag 0.56724 0.45000 0.384
## MA-SR 0.72630 0.46347 0.113
## NF 0.06312 0.37808 0.10734plot(sp.bdp5, ellipse = TRUE)
boxplot(sp.bdp5)
CCA
Run CCA
- Format: 1 matrix of predictors, 1 matrix of species data
- Transform and standardize continuous variables
- Transform species data - sqrt
- Check if unimodal distribution
# Prepare continuous data
seine.env.scaled <- as.data.frame(scale(Seine_sp_sum[,9:13]),center = "TRUE", scale = "TRUE")
seine.env.f <- cbind(seine.env.scaled, Seine_sp_sum[,c("WYType", "ActionPhase", "FlowPulseType", "Month", "Region")])
# Prepare species data
seine.sp <- sqrt.seine[,14:25]
# Check unimodal distribution
# Axis length > 4 = unimodal (CCA)
# 2-4 probably unimodal
# <2 = linear model
decorana(seine.sp, ira=0)##
## Call:
## decorana(veg = seine.sp, ira = 0)
##
## Detrended correspondence analysis with 26 segments.
## Rescaling of axes with 4 iterations.
##
## DCA1 DCA2 DCA3 DCA4
## Eigenvalues 0.4822 0.4194 0.2702 0.2582
## Decorana values 0.5982 0.3530 0.2407 0.1847
## Axis lengths 4.4706 5.3601 4.2156 4.3944# Run CCA
spe.cca <- cca(seine.sp ~.,seine.env.f)
summary(spe.cca)##
## Call:
## cca(formula = seine.sp ~ Cond + WTemp + SecDepth + Turb + DOx + WYType + ActionPhase + FlowPulseType + Month + Region, data = seine.env.f)
##
## Partitioning of scaled Chi-square:
## Inertia Proportion
## Total 2.9507 1.0000
## Constrained 0.4501 0.1525
## Unconstrained 2.5006 0.8475
##
## Eigenvalues, and their contribution to the scaled Chi-square
##
## Importance of components:
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
## Eigenvalue 0.23500 0.10254 0.04697 0.016973 0.01446 0.012272
## Proportion Explained 0.07964 0.03475 0.01592 0.005752 0.00490 0.004159
## Cumulative Proportion 0.07964 0.11439 0.13031 0.136063 0.14096 0.145123
## CCA7 CCA8 CCA9 CCA10 CCA11 CA1
## Eigenvalue 0.007931 0.007318 0.003741 0.002249 0.0006676 0.5052
## Proportion Explained 0.002688 0.002480 0.001268 0.000762 0.0002263 0.1712
## Cumulative Proportion 0.147811 0.150291 0.151559 0.152321 0.1525468 0.3238
## CA2 CA3 CA4 CA5 CA6 CA7 CA8
## Eigenvalue 0.3754 0.27933 0.25931 0.20688 0.19181 0.1800 0.1511
## Proportion Explained 0.1272 0.09466 0.08788 0.07011 0.06501 0.0610 0.0512
## Cumulative Proportion 0.4510 0.54565 0.63353 0.70364 0.76864 0.8296 0.8808
## CA9 CA10 CA11
## Eigenvalue 0.1378 0.11722 0.09658
## Proportion Explained 0.0467 0.03973 0.03273
## Cumulative Proportion 0.9275 0.96727 1.00000
##
## Accumulated constrained eigenvalues
## Importance of components:
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6 CCA7
## Eigenvalue 0.2350 0.1025 0.04697 0.01697 0.01446 0.01227 0.007931
## Proportion Explained 0.5221 0.2278 0.10434 0.03771 0.03212 0.02726 0.017619
## Cumulative Proportion 0.5221 0.7499 0.85424 0.89195 0.92407 0.95133 0.968952
## CCA8 CCA9 CCA10 CCA11
## Eigenvalue 0.007318 0.003741 0.002249 0.0006676
## Proportion Explained 0.016259 0.008311 0.004996 0.0014833
## Cumulative Proportion 0.985210 0.993521 0.998517 1.0000000
##
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
##
##
## Species scores
##
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
## American Shad -0.3864 -0.17890 -0.47388 -0.101298 0.166499 0.217996
## Bigscale Logperch 0.7680 0.28576 -0.05396 -0.004455 0.002668 -0.067560
## Black Crappie 1.0493 0.23224 -0.32185 0.218715 -0.120695 0.067561
## Bluegill 1.1017 0.02645 0.16278 -0.027316 0.046888 0.354338
## Inland Silverside -0.3023 0.01871 0.07074 0.020230 -0.017381 0.007594
## Largemouth Bass 0.2968 -0.22243 0.10671 -0.032732 0.340546 -0.070658
## Sacramento Pikeminnow 0.3742 -1.10405 -0.09626 0.092479 0.145509 0.023398
## Sacramento Sucker 0.6878 -1.65347 -0.11948 -0.097490 -0.497062 -0.100904
## Splittail -0.1431 -1.16417 -0.88934 0.611779 0.727074 -0.202490
## Spotted Bass 0.7244 -0.44496 0.86808 -0.876165 0.354275 -0.327929
## Striped Bass -0.4953 0.19540 -0.89939 -0.453138 -0.013094 0.082728
## Threadfin Shad 0.5665 0.30668 -0.11887 0.031264 -0.035948 -0.163776
##
##
## Site scores (weighted averages of species scores)
##
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
## row1 2.801831 -15.077967 -2.183e+00 -5.457686 -3.003e+01 -8.037389
## row2 1.251255 -10.119668 -2.406e+00 2.220662 -6.361e+00 -3.213392
## row3 1.565944 -9.871410 -2.590e+00 -0.032991 -1.537e+01 -6.458851
## row4 0.714324 -8.269205 -3.681e+00 5.848850 9.393e-01 -4.480817
## row5 1.918276 -11.228901 -1.681e+00 1.533764 -5.001e-01 -1.751285
## row6 -0.631137 -1.355018 1.206e+00 1.265470 3.282e+00 -0.064737
## row7 2.926656 -16.125005 -2.544e+00 -5.743941 -3.438e+01 -8.222299
## row8 0.515756 -6.749413 -4.029e-01 0.241897 -7.785e+00 -1.519882
## row9 0.440822 -1.967547 -3.180e+00 4.412576 5.645e+00 -4.927966
## row10 -1.092873 -1.760016 -4.669e+00 0.714328 1.071e+01 5.440877
## row11 -1.355444 0.327739 -2.351e-01 -1.159112 -1.177e+00 1.134906
## row12 -0.813767 -3.137722 -5.931e+00 6.366238 1.454e+01 0.730435
## row13 -1.016369 0.280351 4.358e-01 0.780116 -4.809e-01 0.621526
## row14 -0.298493 -2.723476 -6.411e-01 3.435126 4.661e+00 -2.185265
## row15 -1.679352 0.114469 -9.244e+00 -10.491435 3.136e+00 8.374594
## row16 -0.253190 -4.586141 -6.642e+00 11.854763 1.586e+01 -5.471308
## row17 -0.745759 -1.395362 1.093e+00 1.542830 1.874e+00 0.371502
## row18 0.636082 -3.198645 -7.696e+00 -0.351403 1.050e+01 -4.054906
## row19 0.446025 -7.782604 -5.532e+00 10.156265 1.373e+01 -7.093745
## row20 1.918328 -12.221870 -1.574e+00 -4.083867 -2.644e+01 -6.106216
## row21 1.884561 -11.997450 -1.925e+00 0.341839 -9.686e+00 -2.475135
## row22 2.553958 -12.998779 -1.465e+00 -4.889246 -2.140e+01 -7.670198
## row23 0.183237 -5.480846 -7.291e-03 -0.077185 -8.435e+00 -1.527994
## row24 1.872919 -9.862282 -9.808e-01 0.263235 1.420e+00 -3.061964
## row25 0.134183 0.648898 4.621e-01 0.931898 1.967e+00 -4.281949
## row26 2.486661 1.440051 6.075e-01 0.108152 2.440e-01 5.000734
## row27 1.830710 1.583449 -6.506e-01 2.055906 -1.582e+00 0.030031
## row28 1.561871 0.842462 6.786e-01 1.528693 -7.551e-01 7.033482
## row29 1.233995 0.462342 -3.225e-01 2.854383 1.478e+00 3.105517
## row30 1.856774 1.526880 -7.009e-01 -0.245404 3.742e-01 -0.470115
## row31 1.304059 0.959535 -2.488e+00 2.442170 1.449e+00 -2.867479
## row32 2.327052 1.465517 -1.513e-01 1.506867 -8.388e-01 3.887416
## row33 1.820491 1.075059 -1.559e+00 0.497931 2.592e-01 -0.941870
## row34 1.214001 1.836053 -2.874e+00 -1.450288 -1.338e+00 -2.198625
## row35 1.262893 -2.169212 2.272e+00 -1.928496 2.355e+01 -5.757663
## row36 2.559755 0.293565 -5.216e+00 10.500593 1.542e+00 1.143540
## row37 -0.948674 0.327594 -1.678e+00 -1.196659 4.587e-01 1.730364
## row38 -0.235468 1.111617 -3.770e+00 -2.244116 -2.218e+00 0.565620
## row39 -1.330009 0.274395 4.044e-01 -0.295670 -1.186e+00 0.945362
## row40 -0.407101 -0.833280 -3.751e+00 -0.939953 3.840e+00 -1.792494
## row41 -1.039609 -0.704069 -2.946e+00 -0.178519 2.809e+00 0.109492
## row42 -0.195846 1.010780 3.154e-01 1.383674 -1.581e+00 -3.499933
## row43 -1.157243 0.385709 3.987e-01 -0.029706 -1.246e+00 0.267109
## row44 -0.060524 -0.818665 -1.499e+00 5.452167 5.839e+00 -1.686174
## row45 -1.074017 0.682197 -1.834e+00 -2.772442 -1.274e+00 0.252763
## row46 1.262893 -2.169212 2.272e+00 -1.928496 2.355e+01 -5.757663
## row47 1.486760 -8.012405 -6.651e-01 3.085200 1.438e+01 -0.548837
## row48 -0.084741 -0.785393 -1.372e+00 2.392075 1.859e+00 -1.757738
## row49 0.222364 0.186591 -1.427e+00 2.697694 5.988e-01 -3.973122
## row50 -0.608004 -0.629808 -3.825e+00 -2.389505 2.419e+00 2.874266
## row51 -0.361687 -2.669391 -6.752e+00 -6.200573 -2.795e-01 4.004187
## row52 -0.698708 -1.056900 -1.609e+00 4.444181 3.654e+00 0.305941
## row53 -0.165915 0.957235 -3.322e+00 -1.932299 4.041e-01 -0.872637
## row54 -0.648497 0.737928 -2.632e+00 -2.271529 -1.302e-01 0.140441
## row55 -0.593396 -3.028121 -5.001e+00 4.916186 7.517e+00 0.089096
## row56 1.850612 -11.944083 -1.573e+00 -3.241833 -2.315e+01 -5.368948
## row57 0.415115 -3.986824 6.316e-01 1.548118 1.009e+01 -0.976264
## row58 -1.737626 0.184630 -1.334e+01 -13.025048 3.792e+00 2.855551
## row59 1.391919 0.003835 -1.488e+00 2.294768 -6.593e-02 -7.448801
## row60 0.481830 -6.697088 -1.270e+00 2.222232 -2.347e+00 -2.452385
## row61 1.080773 -8.308753 -5.883e-01 -1.516122 -1.184e+01 -3.544038
## row62 -0.064894 -4.545020 3.321e-01 -0.818764 -1.082e+01 -1.944216
## row63 1.710281 -9.294254 -9.697e-01 1.745970 6.808e+00 -1.708591
## row64 0.403462 -0.664840 5.571e+00 -13.073457 5.609e+00 -8.709448
## row65 2.166737 -13.073576 -2.262e+00 0.630247 -9.068e+00 -2.453885
## row66 1.314012 -9.866830 -1.058e+00 -2.352463 -1.890e+01 -4.238004
## row67 2.307509 -1.258808 1.831e+00 -0.689860 1.634e+01 3.143694
## row68 -0.872293 -2.960640 -5.254e+00 2.890458 8.343e+00 -0.850989
## row69 1.262893 -2.169212 2.272e+00 -1.928496 2.355e+01 -5.757663
## row70 1.170348 -5.081457 -1.604e+00 3.773581 -2.711e+00 0.812651
## row71 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row72 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row73 1.592292 -10.766912 -2.050e+00 5.448679 1.006e+01 1.906627
## row74 0.603897 -0.921925 5.547e+00 -12.550341 8.165e+00 -7.630364
## row75 2.749752 1.187153 1.044e+00 -0.256609 1.464e+00 7.721069
## row76 2.020781 1.359700 2.244e-01 0.821644 -5.764e-02 2.394571
## row77 1.966777 1.180381 1.817e-01 -0.045764 3.180e-01 4.892474
## row78 1.615087 0.843923 1.066e+00 0.233253 1.345e+00 4.679887
## row79 1.661713 0.932543 9.456e-01 0.298447 1.083e+00 4.250586
## row80 0.907790 -0.035123 -3.192e+00 2.884469 5.221e+00 -1.382564
## row81 1.991517 1.316705 6.749e-01 0.223397 6.468e-02 4.006445
## row82 2.436272 1.627637 -7.700e-01 1.490915 9.038e-01 -0.853407
## row83 1.203791 1.853827 -6.162e-01 1.049202 -1.303e+00 -5.934761
## row84 1.988483 1.481651 -2.499e+00 5.475859 -2.532e+00 -0.732436
## row85 -1.362005 0.341500 -4.000e-01 -1.381851 -1.175e+00 1.183803
## row86 0.372545 0.943640 -1.096e+00 0.825899 -1.005e+00 0.038131
## row87 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row88 -0.667650 0.606831 -7.083e-01 -0.798859 -2.380e-01 -0.714548
## row89 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row90 -0.596629 0.406140 1.246e-01 1.336276 -7.632e-01 1.397892
## row91 -0.086707 0.581486 -5.289e+00 -6.086313 -2.340e-01 -0.550963
## row92 0.018020 0.560682 8.534e-01 1.666565 -1.279e+00 2.702664
## row93 -0.695717 0.517390 -1.921e+00 -2.314471 -9.453e-01 -0.511475
## row94 0.673496 1.671184 -6.339e-01 1.536553 -1.883e+00 -6.783846
## row95 -0.380799 -1.739667 1.199e+00 1.103202 5.403e+00 -0.533653
## row96 0.259359 0.188810 -2.183e-01 1.797141 -6.486e-01 -4.138348
## row97 -0.226392 -2.269629 8.438e-01 1.953240 1.634e+00 2.864758
## row98 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row99 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row100 1.592292 -10.766912 -2.050e+00 5.448679 1.006e+01 1.906627
## row101 -0.582830 -0.763623 2.048e-01 -0.669522 7.760e+00 0.998885
## row102 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row103 1.501284 -4.168859 1.582e+00 -2.475189 1.525e+01 -6.110806
## row104 -0.679127 -2.126703 7.562e-01 2.089665 1.174e+00 0.890399
## row105 2.014526 -12.462379 -2.206e+00 1.906988 -3.999e+00 -1.298479
## row106 0.661589 -7.272594 -7.120e-01 1.928779 -1.665e+00 -0.256070
## row107 -0.793739 -1.964860 -2.167e+00 -0.579653 6.057e+00 5.075073
## row108 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row109 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row110 1.049880 -0.210314 -1.689e+00 -0.224589 -3.263e+00 -3.939295
## row111 -0.542731 -2.681267 7.338e-01 0.625202 -4.577e+00 -0.405961
## row112 -0.222470 0.619095 3.203e-04 0.564389 2.114e-01 -0.273048
## row113 -0.978587 -0.627791 -3.848e+00 -2.222427 3.474e+00 5.445234
## row114 -0.714703 -0.866960 -3.541e+00 -0.408336 4.659e+00 3.716527
## row115 -0.809215 -0.090424 -3.615e+00 -1.448017 3.465e+00 4.878128
## row116 -0.886692 -1.293275 -3.139e+00 1.467167 5.378e+00 2.669760
## row117 -0.615094 0.774982 -5.941e+00 -5.508047 1.325e+00 2.115880
## row118 -0.323886 -0.730385 -3.774e+00 0.355551 5.544e+00 3.325713
## row119 -0.527005 0.382846 -2.048e+00 -0.288337 1.398e+00 1.341994
## row120 1.525517 0.689579 1.497e-01 1.524303 2.132e+00 2.543079
## row121 0.810070 0.947904 1.802e-01 0.343302 -2.665e-01 1.855130
## row122 1.019672 1.457016 -5.765e-01 0.701129 -1.297e+00 -1.894075
## row123 1.104110 1.439219 -3.824e-01 1.787276 -1.592e+00 -1.884403
## row124 1.030014 1.265296 -6.254e-01 0.724502 -7.064e-01 -0.776329
## row125 1.035872 0.672122 -1.507e+00 1.751725 1.749e+00 -0.244764
## row126 1.625890 1.212215 7.033e-01 0.399706 -1.646e-01 3.334204
## row127 2.688685 2.149738 -3.998e-01 0.030802 3.312e-02 -1.572895
## row128 0.701879 1.462252 -4.018e-02 0.933800 -1.093e+00 -3.905487
## row129 2.416140 0.291173 -4.088e+00 8.118963 3.514e+00 -0.693060
## row130 -1.401864 0.052907 -1.763e+00 -2.041305 5.892e-01 3.493068
## row131 -0.743533 0.463382 7.942e-01 1.900931 -1.686e+00 0.097416
## row132 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row133 -0.689949 0.530223 4.250e-01 0.214116 -4.627e-01 -0.850790
## row134 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row135 -0.468798 0.031879 7.222e-01 0.959354 -2.575e+00 -1.781090
## row136 -0.014468 0.536817 -8.894e-01 -0.248697 4.790e-01 1.862374
## row137 -1.093587 0.607235 -1.261e+00 -2.065499 -1.268e+00 0.249387
## row138 0.243040 0.971262 -6.933e-01 0.791609 6.657e-01 -3.962784
## row139 -0.440867 -0.922366 1.371e+00 1.212061 1.369e+00 2.598666
## row140 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row141 -0.871749 -1.421765 1.108e+00 0.509613 -4.466e+00 -0.250945
## row142 1.592292 -10.766912 -2.050e+00 5.448679 1.006e+01 1.906627
## row143 0.855594 0.590385 2.536e+00 -5.895629 2.286e+00 -6.194654
## row144 0.398635 -2.707952 1.018e+00 1.360782 5.972e+00 2.676412
## row145 -1.465156 -0.781076 -4.292e+00 -2.388165 5.156e+00 9.191267
## row146 1.262893 -2.169212 2.272e+00 -1.928496 2.355e+01 -5.757663
## row147 -0.615639 -3.475053 -3.374e+00 -0.048165 6.174e+00 6.743079
## row148 1.016594 -8.651206 -1.035e+00 1.137972 -5.239e+00 -1.169186
## row149 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row150 -1.324322 -0.022819 2.708e-01 0.429113 1.527e-01 2.445354
## row151 0.912023 -10.948110 -7.268e+00 14.903400 2.249e+01 -3.781409
## row152 1.768395 0.987076 9.200e-01 0.664315 -1.376e-01 6.502006
## row153 0.869663 0.769118 8.666e-01 1.214322 -7.499e-01 4.538705
## row154 1.560946 1.059308 5.516e-01 1.144030 -6.441e-01 4.623438
## row155 0.930370 0.585415 1.402e-01 1.725763 -7.470e-01 1.244485
## row156 1.557501 0.842443 -5.319e-01 1.336338 -2.756e+00 -1.626444
## row157 0.432073 0.645955 1.036e+00 0.698767 4.784e-01 1.517448
## row158 2.370898 1.573322 -2.731e-01 1.440586 -8.482e-01 2.911194
## row159 1.746477 1.628260 -5.053e-01 1.586604 -1.179e+00 -0.584950
## row160 1.548757 0.911926 -5.954e-01 0.989744 1.042e-01 -4.214069
## row161 2.951936 0.558858 -2.293e+00 5.370703 3.286e+00 4.017075
## row162 -1.065292 0.240786 4.719e-01 0.761223 -4.457e-01 0.829225
## row163 -1.151191 -0.331027 1.339e+00 1.391569 -6.738e-01 0.679199
## row164 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row165 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row166 -1.175373 0.142165 2.303e-01 -0.797286 4.048e-01 0.602507
## row167 -1.059353 0.354808 1.258e+00 1.231822 -1.281e+00 -0.238065
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## row1498 -0.888883 -1.328815 1.015e+00 1.779474 3.528e-01 0.796555
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## row1505 0.798115 0.509754 1.146e+00 0.114687 3.052e+00 0.997750
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## row1507 0.564690 1.161264 -2.001e-01 1.651675 -4.821e-01 -3.690127
## row1508 1.806548 1.837909 -1.818e+00 3.597212 -2.758e+00 -2.738868
## row1509 1.212556 0.121254 3.287e-02 -1.071122 5.003e+00 7.339246
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## row1516 -0.230324 -0.791617 1.823e+00 -0.100592 9.051e+00 -2.022417
## row1517 1.303281 -12.748400 -7.843e+00 11.916512 8.657e+00 -7.605306
## row1518 -1.373419 -0.091550 -4.231e+00 -5.389435 5.075e-01 3.573115
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## row1524 2.860742 1.856300 -4.283e-01 1.041091 -6.387e-01 2.007874
## row1525 2.114438 1.023193 8.879e-01 0.005970 1.963e+00 4.410645
## row1526 1.577748 1.135909 4.993e-01 0.424455 1.129e+00 0.893075
## row1527 0.911854 0.898910 9.540e-01 0.676768 -4.835e-01 3.241523
## row1528 0.997619 1.564878 -2.569e-01 1.155963 -1.329e+00 -3.876124
## row1529 1.146778 1.407849 -4.797e-01 2.066689 -1.678e+00 -1.194983
## row1530 2.926656 -16.125005 -2.544e+00 -5.743941 -3.438e+01 -8.222299
## row1531 1.372693 -5.035112 8.315e-01 0.530563 1.906e+01 -3.202899
## row1532 2.926656 -16.125005 -2.544e+00 -5.743941 -3.438e+01 -8.222299
## row1533 3.082416 -4.339357 1.848e+01 -51.621892 2.450e+01 -26.721823
## row1534 -1.549397 0.734521 -5.111e+00 -7.743360 -1.107e+00 2.580294
## row1535 1.812362 0.963104 -1.508e+00 3.552901 -3.893e-01 3.556479
## row1536 2.824012 -15.712844 -2.506e+00 -4.882970 -3.096e+01 -7.443151
## row1537 1.448512 -7.014088 -1.633e-01 2.228604 1.595e+01 -1.438772
## row1538 -0.947646 -5.585396 -8.715e+00 18.618364 2.454e+01 -7.940722
## row1539 -1.644123 -1.744641 -1.009e+01 -5.968260 1.151e+01 17.763734
## row1540 2.471649 1.554113 -7.382e-01 0.600371 3.700e+00 -6.194030
## row1541 1.443682 1.844572 -1.104e+00 1.793667 -1.143e+00 -6.683720
## row1542 1.631884 1.705992 -2.932e-01 0.954316 -1.030e+00 -2.375337
## row1543 0.896519 1.330230 -2.208e-01 1.735396 -1.537e+00 -1.626376
## row1544 0.326923 0.913500 2.238e-01 1.949852 -1.615e+00 0.254766
## row1545 0.919435 1.331407 1.982e-01 0.906987 -9.515e-01 -1.523480
## row1546 0.376971 1.128532 -3.788e-01 2.523372 -2.147e+00 -1.890201
## row1547 1.578187 1.154992 -9.322e-01 3.804855 -2.550e+00 3.645098
## row1548 2.926656 -16.125005 -2.544e+00 -5.743941 -3.438e+01 -8.222299
## row1549 -1.542054 0.019240 -5.605e+00 -6.189682 2.180e+00 6.309432
## row1550 -1.326900 -0.036703 1.872e-01 0.377527 2.444e-01 2.568875
## row1551 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1552 2.926656 -16.125005 -2.544e+00 -5.743941 -3.438e+01 -8.222299
## row1553 1.262893 -2.169212 2.272e+00 -1.928496 2.355e+01 -5.757663
## row1554 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1555 2.926656 -16.125005 -2.544e+00 -5.743941 -3.438e+01 -8.222299
## row1556 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1557 1.780970 1.474059 -7.698e-01 2.108665 -4.864e-01 -1.467602
## row1558 1.978777 1.047335 4.392e-01 0.950755 8.739e-01 4.168976
## row1559 2.148783 1.311782 -8.902e-01 2.291322 1.008e+00 -0.850675
## row1560 1.562456 1.591659 -7.916e-01 2.259917 -1.877e+00 -1.433056
## row1561 0.596778 1.161230 5.766e-02 1.617273 -1.475e+00 -1.237110
## row1562 1.106050 1.545119 -1.219e+00 3.129536 -2.581e+00 -3.017452
## row1563 2.018491 1.118130 -1.053e+00 3.590738 -7.322e-01 3.040200
## row1564 1.982480 -11.509658 -1.718e+00 1.027203 -2.646e+00 -2.206588
## row1565 -1.137647 0.045449 1.551e+00 1.010095 2.404e-01 0.247226
## row1566 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1567 -0.831156 -1.578897 1.069e+00 0.442782 -4.785e+00 -0.336134
## row1568 1.262893 -2.169212 2.272e+00 -1.928496 2.355e+01 -5.757663
## row1569 -1.347219 -0.146101 -4.710e-01 -0.028936 9.663e-01 3.542143
## row1570 1.592292 -10.766912 -2.050e+00 5.448679 1.006e+01 1.906627
## row1571 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1572 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1573 0.063511 -5.042061 2.086e-01 -1.030164 -1.183e+01 -2.213686
## row1574 1.957473 0.900087 9.512e-01 0.178937 1.888e+00 4.643914
## row1575 2.641721 1.147534 8.499e-01 -0.111827 2.042e+00 5.795023
## row1576 1.847123 0.825350 6.280e-01 1.718347 -6.486e-01 8.820195
## row1577 0.204607 0.478104 1.469e+00 0.731805 -4.973e-01 4.517294
## row1578 1.101107 1.329717 3.713e-01 0.586167 -5.475e-01 -0.413979
## row1579 1.026610 1.151739 -1.308e+00 4.415506 -3.103e+00 1.204332
## row1580 1.366275 0.848936 -8.864e-01 1.691624 1.626e+00 1.424058
## row1581 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1582 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1583 -0.897265 -3.037347 -6.906e+00 -1.410576 8.212e+00 4.741135
## row1584 2.019792 -12.483523 -2.208e+00 1.862819 -4.174e+00 -1.338450
## row1585 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1586 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1587 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1588 2.926656 -16.125005 -2.544e+00 -5.743941 -3.438e+01 -8.222299
## row1589 2.174730 -13.105675 -2.265e+00 0.563194 -9.334e+00 -2.514565
## row1590 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1591 2.455962 -6.737689 7.741e+00 -23.575927 8.726e+00 -15.114723
## row1592 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1593 -0.535805 -0.594216 4.422e+00 -7.879764 3.213e+00 -4.077428
## row1594 2.449714 0.738136 1.610e+00 -0.420277 2.426e+00 9.844041
## row1595 2.126993 0.991766 -6.820e-01 -2.566980 3.912e+00 3.989673
## row1596 1.231074 0.997345 2.120e-01 0.197557 3.757e+00 -4.518197
## row1597 2.247341 1.026096 -2.227e-01 2.211251 5.627e-01 5.218665
## row1598 0.571021 0.710924 -5.243e-01 0.027733 4.988e-01 2.208192
## row1599 0.782178 0.389980 -7.608e-01 4.024737 8.444e-01 0.963880
## row1600 1.314974 0.708955 -2.894e-01 2.929524 1.404e-01 3.137294
## row1601 2.069453 -12.682938 -2.226e+00 1.446256 -5.828e+00 -1.715424
## row1602 2.410571 2.990772 -2.531e+00 1.842027 -2.486e+00 -13.345591
## row1603 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1604 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1605 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1606 -1.052197 0.360244 1.251e+00 1.233080 -1.283e+00 -0.265097
## row1607 -1.286189 0.182489 1.506e+00 1.191931 -1.202e+00 0.618801
## row1608 2.096643 -12.792119 -2.236e+00 1.218187 -6.734e+00 -1.921819
## row1609 3.399705 -0.655117 3.017e+00 -1.729451 1.088e+01 15.846201
## row1610 0.952781 -6.832762 -7.712e-02 -5.823064 3.081e+00 -1.625667
##
##
## Site constraints (linear combinations of constraining variables)
##
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
## row1 1.4098952 -4.8497337 -1.384125 0.2548256 -1.199678 -0.7107068
## row2 -0.1396282 -2.5357161 -1.390291 1.8857057 2.918085 -0.6382765
## row3 -0.3444270 -2.2743655 -1.868970 1.4582290 1.470042 0.0661155
## row4 0.7849248 -2.5850373 -1.873212 2.2077212 -0.023303 -1.3481891
## row5 1.6274663 -3.7932077 -1.266080 0.7247394 0.154479 -0.5774650
## row6 1.8709570 -2.7256911 -1.201177 1.2212492 1.608536 -0.6697711
## row7 -0.4529415 -2.8322310 -1.946960 1.2281330 0.755566 -0.0687114
## row8 -0.4604390 -2.9201379 -1.670685 1.3593964 0.896601 -0.2529217
## row9 -0.3669850 -2.4257480 -2.198107 1.2888169 1.033598 0.0198197
## row10 -0.3274349 -2.3113750 -2.092211 1.4085053 1.350697 -0.1453553
## row11 -0.4342892 -2.7808333 -2.384483 1.0615661 0.516911 -0.0485038
## row12 -0.3528577 -2.3259323 -1.848000 1.4689458 1.407777 0.0269737
## row13 -0.3548872 -2.4165291 -2.646587 1.0810322 0.788422 0.0213392
## row14 -0.3593349 -2.3479113 -1.945511 1.4113181 1.294182 0.0642545
## row15 -0.2893625 -2.0812823 -3.169773 0.9495896 0.782050 0.2232587
## row16 -0.2893292 -1.9831015 -1.939106 1.5332225 1.731471 0.1733469
## row17 -0.2218520 -2.8583471 -1.397179 1.8123030 2.290765 -0.5510982
## row18 -0.2191261 -2.8577230 -1.396878 1.7412813 2.437364 -0.5554191
## row19 -0.3882824 -2.4725801 -1.885061 1.3782700 1.184634 0.0671922
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## row1522 0.2326700 -0.5015245 -0.048711 1.0188020 -2.199562 -0.3310266
## row1523 1.1177868 -1.4883328 0.605953 -0.3698066 -1.721584 0.4955585
## row1524 1.4674347 0.2003891 0.005828 0.1318157 -0.644257 0.4232530
## row1525 1.4963258 0.2630240 -0.187786 0.0482014 -0.348283 0.6111244
## row1526 1.4960998 0.3970157 -0.056221 0.0590926 -0.304499 0.6842400
## row1527 0.5681290 1.2114525 -0.738884 1.3728605 -0.985303 0.0481132
## row1528 0.5588679 1.1582344 -0.893858 1.1813719 -1.236248 -0.2694948
## row1529 0.4914113 0.8184988 -0.530979 1.2751383 -0.985591 0.1997346
## row1530 1.0563347 -1.8503353 0.673317 -0.4678365 -2.007435 0.2983902
## row1531 0.2207618 -0.6003436 -0.044424 0.9969379 -2.265291 -0.4314201
## row1532 1.1119250 -1.5580713 0.570818 -0.3924057 -1.793553 0.4056939
## row1533 1.2072847 -1.1957300 0.417653 -0.2778895 -1.372009 0.2831626
## row1534 -0.7095037 -0.5906230 0.295364 0.6005439 0.525008 0.2778584
## row1535 0.5210482 0.7032356 -0.390273 1.5331370 -0.048868 0.8537603
## row1536 0.9947472 -2.0298549 0.721262 -0.5615846 -2.323689 0.5084995
## row1537 -0.6104128 -0.2766642 0.384239 0.9216703 1.005181 -0.0666153
## row1538 -0.7717733 -0.8861450 0.461110 0.5684496 0.277539 0.2093300
## row1539 1.0828906 -1.6178396 0.652728 -0.4096270 -1.893950 0.5474330
## row1540 1.3018842 -0.7663364 0.527133 -0.0283365 -0.770385 0.2567591
## row1541 1.3864585 0.7960660 0.487624 0.8675864 -0.372705 0.6973816
## row1542 1.5299292 1.1394186 -0.017733 0.7750837 -0.028662 -0.2631869
## row1543 1.5375731 1.5021573 0.316006 0.9622960 0.513180 0.7443120
## row1544 0.6324700 2.3136998 -0.399080 2.2668336 -0.201265 -0.3945598
## row1545 0.6025253 2.0579536 -0.609991 2.0491978 -0.588364 -0.8114044
## row1546 0.5092234 1.6499228 -0.426195 1.9644714 -0.646293 -0.3242045
## row1547 0.4595569 1.0669762 -0.459056 1.9853891 -0.400755 -0.0147441
## row1548 0.9423948 -1.5527239 0.848367 0.0258440 -2.311381 0.0342390
## row1549 -0.7769967 -0.1982012 0.479753 1.1903391 0.485918 -0.2459363
## row1550 -0.9978674 0.0002678 0.026042 0.7443596 -1.035971 0.4749208
## row1551 0.1868731 0.0139145 0.120034 1.6384783 -2.116963 -0.7951776
## row1552 1.0925085 -0.8929672 0.786127 0.2929854 -1.509705 0.0004776
## row1553 1.1439669 -0.6753562 0.643300 0.3264500 -1.327686 -0.0035220
## row1554 0.2464304 0.2827244 0.473789 1.2961726 -1.809100 -0.7370684
## row1555 1.1615782 -0.5800152 0.878960 -0.1566691 -1.343984 0.1182478
## row1556 -0.9391065 0.2936480 0.393063 0.3995226 -0.708618 0.5948550
## row1557 1.5091269 0.9652596 0.477061 0.3978984 0.180715 0.0705435
## row1558 1.4937648 0.8813449 0.525308 0.3932702 0.125116 0.0276243
## row1559 1.4582292 0.6381275 0.546532 0.3397738 -0.075359 -0.1611581
## row1560 0.5288141 1.4075603 -0.223639 1.6162940 -0.745467 -0.7237836
## row1561 0.5329482 1.5367803 -0.148358 1.6083904 -0.920334 -0.9766954
## row1562 0.5492645 1.6446748 -0.199897 1.6233979 -0.778068 -0.7502969
## row1563 0.5339843 1.5157598 -0.202133 1.6354880 -0.693455 -0.5397528
## row1564 1.0494202 -1.2119334 1.057381 -0.2921379 -1.851176 -0.1945963
## row1565 -0.7281603 0.0605465 0.589831 0.7098293 0.550431 -0.0486357
## row1566 -0.9449936 0.1989592 0.213237 0.3134180 -0.901835 0.4798029
## row1567 0.1961240 -0.0157901 0.332982 1.1440053 -2.229669 -0.8666490
## row1568 1.1429493 -0.7150786 0.878266 -0.1693932 -1.494464 -0.0009231
## row1569 -0.8133734 -0.4039020 0.820618 0.6784183 0.193657 -0.2797637
## row1570 0.9781533 -1.5572662 1.083020 -0.4060881 -2.261639 -0.2532955
## row1571 -0.9291615 -0.9380155 0.637190 0.3746965 -0.624290 -0.2628619
## row1572 -1.1184715 -0.6094245 0.289339 0.0352688 -1.876429 0.4076388
## row1573 0.0946977 -0.5479901 0.348131 0.9725000 -2.833542 -1.0362940
## row1574 1.7299167 0.3691110 0.380605 1.1500693 0.144508 1.1439390
## row1575 1.6945195 0.2788222 0.473779 1.0825089 -0.059482 1.0789218
## row1576 1.6878268 0.2333786 0.544337 1.0643794 -0.128243 0.8280657
## row1577 0.7166773 0.8386426 -0.057168 2.3439981 -0.913746 0.2830932
## row1578 0.6866387 0.6367005 -0.087886 2.3079573 -0.975573 0.4169224
## row1579 0.6446162 0.3687286 -0.019956 2.2957995 -0.981457 0.5741176
## row1580 0.6537176 0.3998678 0.109623 2.3605808 -0.905880 0.3855809
## row1581 -0.6114195 -0.9551691 0.822391 1.3564896 0.225759 1.0147998
## row1582 0.3595334 -0.8813193 0.485740 1.8370115 -2.340362 0.0796570
## row1583 -0.5611040 -0.8680415 0.834679 1.4628421 0.511519 0.6980852
## row1584 1.2245975 -2.0609189 1.120331 0.4072646 -2.010103 0.6820136
## row1585 -0.7857312 -0.8579866 1.008163 0.9207256 0.740550 0.2237827
## row1586 -0.9819120 -0.5465660 0.547149 0.5181446 -0.643698 0.9488642
## row1587 0.2313370 -0.4600289 0.496241 1.3924441 -1.664328 -0.4130447
## row1588 1.1794691 -1.2405040 1.227970 0.1409541 -0.732908 0.2267731
## row1589 1.1151417 -1.4929860 1.131551 -0.0027263 -1.219538 0.3269196
## row1590 -0.8302519 -0.9162294 0.955642 0.8131351 0.445898 0.5531974
## row1591 1.0855135 -1.4948469 1.182619 -0.0038177 -1.398868 0.6009602
## row1592 0.1870943 -0.6378348 0.508113 1.3157111 -1.913472 -0.3661399
## row1593 -0.8143397 -1.0739207 0.881285 0.8160439 0.456263 0.0564915
## row1594 1.2978172 -0.7211647 0.352682 0.1377445 -1.024848 0.3498301
## row1595 1.2128998 -1.0626953 0.495118 0.0413802 -1.351177 0.4858847
## row1596 1.2093529 -1.0385862 0.491575 -0.0217670 -1.328544 0.5205755
## row1597 0.3561529 0.2424203 -0.647752 1.0983150 -2.165915 -0.3362619
## row1598 0.3351199 -0.1240138 -0.144259 1.3718922 -1.442452 -0.2182960
## row1599 0.3000572 -0.6144025 -0.280688 1.3809835 -1.056695 0.3826929
## row1600 0.2734628 -0.5787707 -0.111450 1.3375278 -1.398137 0.0747617
## row1601 1.0661816 -1.7360463 1.103264 -0.1016874 -1.538901 0.2833396
## row1602 1.0471384 -1.8538641 1.040830 -0.1426140 -1.741431 0.2195742
## row1603 -0.8479424 -1.0366868 0.804147 0.7711834 0.116065 0.4783086
## row1604 -0.8500427 -1.1334620 0.902128 0.7558784 0.274090 0.2795018
## row1605 -0.9472957 -1.5253324 0.926925 0.5906845 -0.281650 0.3794476
## row1606 0.1256991 -0.8642147 0.383099 1.1525174 -2.384631 -0.2279689
## row1607 -1.1243216 -1.1430920 0.428301 0.2005880 -1.574078 1.0791166
## row1608 1.0671535 -1.6818312 1.099151 -0.1024564 -1.532860 0.3951514
## row1609 1.1146348 -1.5424359 1.062711 0.0298561 -1.391293 0.2181981
## row1610 1.1069364 -1.3262685 0.369936 -0.3976047 -1.810524 0.9509688
##
##
## Biplot scores for constraining variables
##
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
## Cond -0.117619 0.22693 0.25706 0.416061 -0.1506079 -0.08766
## WTemp 0.038643 0.37088 -0.17335 -0.009927 0.2804837 -0.16995
## SecDepth -0.200444 -0.06514 0.12341 0.062720 0.0294296 -0.02608
## Turb 0.248145 0.37962 -0.74633 -0.183637 0.0179697 0.17087
## DOx -0.369419 -0.15201 0.02407 -0.189158 -0.2869284 0.36434
## WYTypeC -0.231771 0.20818 0.29458 -0.141069 -0.0610973 -0.23661
## WYTypeD 0.046539 0.08517 0.18264 -0.321318 0.1665982 0.04898
## WYTypeW 0.284486 -0.26470 -0.26487 0.483691 0.0546413 0.41425
## ActionPhaseDuring -0.044047 0.24752 0.03555 0.124087 0.0544190 -0.25556
## ActionPhasePost 0.088072 0.02015 0.27277 0.093048 -0.0506486 0.24158
## FlowPulseTypeMA-Ag -0.030423 -0.04067 0.18255 0.202802 -0.1832027 -0.01240
## FlowPulseTypeMA-SR -0.037563 0.02918 -0.24947 -0.028772 -0.0872875 -0.23922
## FlowPulseTypeNF -0.008808 -0.03252 0.11849 0.021575 0.2575866 0.13455
## Month.L 0.105727 0.15753 0.44508 0.047691 -0.0006106 0.30646
## Month.Q 0.125203 -0.31039 -0.09590 0.124429 0.0812208 0.08044
## Month.C -0.051754 -0.14461 -0.29420 0.055514 -0.1081123 0.10608
## Month^4 -0.043859 0.28762 -0.02163 -0.070557 -0.2064611 0.22501
## Month^5 -0.030428 -0.01385 0.07113 0.075663 0.0313348 -0.20011
## RegionCentralYolo 0.848411 -0.13670 0.20310 -0.324753 0.0614219 0.05753
## RegionLowerSacRiver -0.413952 -0.09856 0.30189 0.275661 0.2818543 -0.17123
## RegionLowerYolo 0.189677 0.25997 -0.13306 0.386443 -0.3797470 -0.30779
##
##
## Centroids for factor constraints
##
## CCA1 CCA2 CCA3 CCA4 CCA5
## WYTypeBN -0.17647 0.048585 -0.16155 -0.245828 -0.165890
## WYTypeC -0.43526 0.390952 0.55320 -0.264922 -0.114738
## WYTypeD 0.13718 0.251037 0.53834 -0.947101 0.491057
## WYTypeW 0.37557 -0.349444 -0.34968 0.638557 0.072136
## ActionPhasePre -0.04792 -0.377356 -0.39304 -0.293321 -0.013814
## ActionPhaseDuring -0.05344 0.300283 0.04313 0.150541 0.066020
## ActionPhasePost 0.15239 0.034866 0.47197 0.161002 -0.087638
## FlowPulseTypeCA 0.11555 0.101787 -0.24790 -0.339457 -0.170234
## FlowPulseTypeMA-Ag -0.07141 -0.095470 0.42850 0.476047 -0.430042
## FlowPulseTypeMA-SR -0.12341 0.095856 -0.81964 -0.094530 -0.286786
## FlowPulseTypeNF -0.00816 -0.030125 0.10978 0.019988 0.238645
## Month6 0.37335 -1.268759 -2.95658 -0.609195 0.595966
## Month7 -0.22069 -1.364878 -0.99321 0.434051 0.404732
## Month8 -0.03986 0.135148 -0.14606 -0.100079 -0.144112
## Month9 -0.07633 0.340913 0.28231 -0.008719 -0.066093
## Month10 0.16673 -0.086695 0.47902 -0.030970 0.330074
## Month11 0.81082 -0.566422 0.50312 1.171646 -0.917492
## RegionCacheSloughComplex -0.84781 0.008399 -0.50148 -0.354650 0.001371
## RegionCentralYolo 1.38106 -0.222519 0.33060 -0.528637 0.099983
## RegionLowerSacRiver -0.77813 -0.185259 0.56747 0.518174 0.529815
## RegionLowerYolo 0.40999 0.561918 -0.28761 0.835292 -0.820819
## CCA6
## WYTypeBN -0.37304
## WYTypeC -0.44435
## WYTypeD 0.14437
## WYTypeW 0.54688
## ActionPhasePre 0.06020
## ActionPhaseDuring -0.31005
## ActionPhasePost 0.41800
## FlowPulseTypeCA 0.01802
## FlowPulseTypeMA-Ag -0.02911
## FlowPulseTypeMA-SR -0.78597
## FlowPulseTypeNF 0.12466
## Month6 -1.90466
## Month7 -1.22958
## Month8 0.22543
## Month9 -0.16103
## Month10 -0.08396
## Month11 3.50201
## RegionCacheSloughComplex 0.49413
## RegionCentralYolo 0.09365
## RegionLowerSacRiver -0.32187
## RegionLowerYolo -0.66528Interpretation
- Interpretation of CCA axis, terms
- global model
- axis
- terms (order matters)
- Can use a step model to create final CCA model
# Test the significance of the CCA
anova(spe.cca)## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
##
## Model: cca(formula = seine.sp ~ Cond + WTemp + SecDepth + Turb + DOx + WYType + ActionPhase + FlowPulseType + Month + Region, data = seine.env.f)
## Df ChiSquare F Pr(>F)
## Model 21 0.45012 13.612 0.001 ***
## Residual 1588 2.50057
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(spe.cca, by = "axis")## Permutation test for cca under reduced model
## Forward tests for axes
## Permutation: free
## Number of permutations: 999
##
## Model: cca(formula = seine.sp ~ Cond + WTemp + SecDepth + Turb + DOx + WYType + ActionPhase + FlowPulseType + Month + Region, data = seine.env.f)
## Df ChiSquare F Pr(>F)
## CCA1 1 0.23500 150.1778 0.001 ***
## CCA2 1 0.10254 65.5290 0.001 ***
## CCA3 1 0.04697 30.0148 0.001 ***
## CCA4 1 0.01697 10.8465 0.001 ***
## CCA5 1 0.01446 9.2403 0.003 **
## CCA6 1 0.01227 7.8424 0.012 *
## CCA7 1 0.00793 5.0680 0.322
## CCA8 1 0.00732 4.6768 0.372
## CCA9 1 0.00374 2.3906 0.996
## CCA10 1 0.00225 1.4370 1.000
## CCA11 1 0.00067 0.4267 1.000
## Residual 1598 2.50057
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(spe.cca, by = "terms")## Permutation test for cca under reduced model
## Terms added sequentially (first to last)
## Permutation: free
## Number of permutations: 999
##
## Model: cca(formula = seine.sp ~ Cond + WTemp + SecDepth + Turb + DOx + WYType + ActionPhase + FlowPulseType + Month + Region, data = seine.env.f)
## Df ChiSquare F Pr(>F)
## Cond 1 0.01641 10.4233 0.001 ***
## WTemp 1 0.01817 11.5391 0.001 ***
## SecDepth 1 0.01013 6.4362 0.001 ***
## Turb 1 0.04757 30.2125 0.001 ***
## DOx 1 0.03784 24.0332 0.001 ***
## WYType 3 0.03635 7.6951 0.001 ***
## ActionPhase 2 0.04705 14.9384 0.001 ***
## FlowPulseType 3 0.01794 3.7975 0.001 ***
## Month 5 0.04407 5.5971 0.001 ***
## Region 3 0.17458 36.9552 0.001 ***
## Residual 1588 2.50057
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(spe.cca, by = 'margin')## Permutation test for cca under reduced model
## Marginal effects of terms
## Permutation: free
## Number of permutations: 999
##
## Model: cca(formula = seine.sp ~ Cond + WTemp + SecDepth + Turb + DOx + WYType + ActionPhase + FlowPulseType + Month + Region, data = seine.env.f)
## Df ChiSquare F Pr(>F)
## Cond 1 0.01137 7.2189 0.001 ***
## WTemp 1 0.03187 20.2370 0.001 ***
## SecDepth 1 0.00196 1.2424 0.227
## Turb 1 0.03110 19.7505 0.001 ***
## DOx 1 0.00738 4.6869 0.001 ***
## WYType 3 0.04176 8.8402 0.001 ***
## ActionPhase 2 0.01041 3.3061 0.001 ***
## FlowPulseType 3 0.01534 3.2475 0.001 ***
## Month 5 0.03669 4.6597 0.001 ***
## Region 3 0.17458 36.9552 0.001 ***
## Residual 1588 2.50057
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Forward stepping
cca.step <- ordistep(cca(seine.sp ~ 1, data = seine.env.f), scope = formula(spe.cca),
direction = "forward", pstep = 1000)##
## Start: seine.sp ~ 1
##
## Df AIC F Pr(>F)
## + Region 3 2359.0 49.2542 0.005 **
## + Turb 1 2465.6 31.4198 0.005 **
## + WYType 3 2472.6 9.4504 0.005 **
## + DOx 1 2475.4 21.4291 0.005 **
## + Month 5 2476.2 5.7275 0.005 **
## + WTemp 1 2486.9 9.8683 0.005 **
## + ActionPhase 2 2487.0 5.8779 0.005 **
## + Cond 1 2487.8 8.9946 0.005 **
## + SecDepth 1 2490.6 6.1428 0.005 **
## + FlowPulseType 3 2493.7 2.3581 0.005 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region
##
## Df AIC F Pr(>F)
## + Turb 1 2335.7 25.4795 0.005 **
## + Month 5 2341.7 5.4886 0.005 **
## + WYType 3 2342.8 7.4248 0.005 **
## + WTemp 1 2350.8 10.2736 0.005 **
## + Cond 1 2351.9 9.0765 0.005 **
## + ActionPhase 2 2352.1 5.4799 0.005 **
## + DOx 1 2355.2 5.8087 0.005 **
## + FlowPulseType 3 2357.5 2.5164 0.005 **
## + SecDepth 1 2359.0 2.0408 0.070 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + Turb
##
## Df AIC F Pr(>F)
## + WYType 3 2319.0 7.5629 0.005 **
## + Month 5 2319.3 5.2920 0.005 **
## + ActionPhase 2 2328.6 5.5314 0.005 **
## + Cond 1 2328.6 9.0207 0.005 **
## + WTemp 1 2328.8 8.8942 0.005 **
## + DOx 1 2333.0 4.6301 0.005 **
## + FlowPulseType 3 2336.4 1.7379 0.025 *
## + SecDepth 1 2336.9 0.7485 0.630
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + Turb + WYType
##
## Df AIC F Pr(>F)
## + Month 5 2302.7 5.2710 0.005 **
## + ActionPhase 2 2310.1 6.4696 0.005 **
## + WTemp 1 2313.6 7.4466 0.005 **
## + Cond 1 2314.1 6.8798 0.005 **
## + FlowPulseType 3 2315.1 3.2973 0.005 **
## + DOx 1 2315.9 5.0778 0.005 **
## + SecDepth 1 2320.1 0.9112 0.460
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + Turb + WYType + Month
##
## Df AIC F Pr(>F)
## + WTemp 1 2284.6 20.0350 0.005 **
## + Cond 1 2298.1 6.5435 0.005 **
## + FlowPulseType 3 2298.7 3.3166 0.005 **
## + ActionPhase 2 2299.9 3.3728 0.005 **
## + DOx 1 2299.9 4.7293 0.005 **
## + SecDepth 1 2303.5 1.1985 0.255
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + Turb + WYType + Month + WTemp
##
## Df AIC F Pr(>F)
## + Cond 1 2279.5 7.0339 0.005 **
## + FlowPulseType 3 2280.9 3.2168 0.005 **
## + ActionPhase 2 2281.0 3.7848 0.005 **
## + DOx 1 2281.7 4.8599 0.005 **
## + SecDepth 1 2285.4 1.1592 0.335
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + Turb + WYType + Month + WTemp + Cond
##
## Df AIC F Pr(>F)
## + FlowPulseType 3 2275.2 3.4153 0.005 **
## + ActionPhase 2 2276.1 3.6893 0.005 **
## + DOx 1 2276.7 4.7404 0.005 **
## + SecDepth 1 2280.3 1.1853 0.315
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + Turb + WYType + Month + WTemp + Cond + FlowPulseType
##
## Df AIC F Pr(>F)
## + DOx 1 2272.0 5.1585 0.005 **
## + ActionPhase 2 2272.3 3.4221 0.005 **
## + SecDepth 1 2276.1 1.0563 0.330
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + Turb + WYType + Month + WTemp + Cond + FlowPulseType + DOx
##
## Df AIC F Pr(>F)
## + ActionPhase 2 2269.5 3.1931 0.005 **
## + SecDepth 1 2272.9 1.0143 0.430
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + Turb + WYType + Month + WTemp + Cond + FlowPulseType + DOx + ActionPhase
##
## Df AIC F Pr(>F)
## + SecDepth 1 2270.2 1.2424 0.25Plot
- Plot CCA
plot(spe.cca, choices = c(1,2), display = c('wa', 'sp', 'bp'), scaling = 2)
# Plot the CCA
cca.biplot = function(cca){
#find plot dimensions (changed these so all the points would fit)
xmin = min(summary((cca))$species[, 1]) * 1.6
xmax = max(summary((cca))$species[, 1]) * 1.4
ymin = min(summary((cca))$species[, 2]) * 1.2
ymax = max(summary((cca))$species[, 2]) * 2.2
par(bty='l')
# plot(cca,disp='species',scaling=1) #scale to show species the best
plot(summary((cca))$species[, 1], summary((cca))$species[, 2],
type = 'n', xlim = c(xmin, xmax), ylim = c(ymin, ymax),
ylab = 'CA2 (8.0% Variation Explained)', xlab = 'CA1 (3.5% Variation Explained)')
axis(side = 1, lwd = 2)
axis(side = 2, lwd = 2)
box(lwd = 2)
#draw origin lines
segments(-2, 0, 2, 0, lwd = 1, lty = 3)
segments(0, -4, 0, 2, lwd = 1, lty = 3)
#Add species names
text(summary((cca))$species[, 1],summary((cca))$species[, 2], labels = rownames(summary((cca))$species), cex = 0.8)
#define continuous variables possibly used
cont.vars=c('Cond','WTemp','DOx','SecDepth','Turb')
bi.names = row.names(summary(cca)$biplot) #names of environmental variables
# centroid.names=row.names(summary(cca)$centroid)
centroid.names = data.frame(Rows = rownames(summary((cca))$centroid))
#Pain in the a$$ way to do this, but I created abbreviated names for each level of
#my categorical variable so that they would look nicer when plotted
#Else I would have names like HabitatC on the biplot
#
centroid.names$New[centroid.names$Rows == 'ActionPhasePre'] = 'PreAction'
centroid.names$New[centroid.names$Rows == 'ActionPhaseDuring'] = 'DuringAction'
centroid.names$New[centroid.names$Rows == 'ActionPhasePost'] = 'PostAction'
centroid.names$New[centroid.names$Rows == 'WYTypeC'] = 'CriticalWY'
centroid.names$New[centroid.names$Rows == 'WYTypeD'] = 'DryWY'
centroid.names$New[centroid.names$Rows == 'WYTypeW'] = 'WetWY'
centroid.names$New[centroid.names$Rows == 'FlowPulseTypeMA-Ag'] = 'AgPulse'
centroid.names$New[centroid.names$Rows == 'FlowPulseTypeMA-SR'] = 'SRPulse'
centroid.names$New[centroid.names$Rows == 'FlowPulseTypeNF'] = 'NoFA'
centroid.names$New[centroid.names$Rows == 'Month4'] = 'Apr'
centroid.names$New[centroid.names$Rows == 'Month5'] = 'May'
centroid.names$New[centroid.names$Rows == 'Month6'] = 'June'
centroid.names$New[centroid.names$Rows == 'Month7'] = 'July'
centroid.names$New[centroid.names$Rows == 'Month8'] = 'Aug'
centroid.names$New[centroid.names$Rows == 'Month9'] = 'Sep'
centroid.names$New[centroid.names$Rows == 'Month10'] = 'Oct'
centroid.names$New[centroid.names$Rows == 'Month11'] = 'Nov'
centroid.names$New[centroid.names$Rows == 'Month12'] = 'Dec'
centroid.names$New[centroid.names$Rows == 'Month1'] = 'Jan'
centroid.names$New[centroid.names$Rows == 'Month2'] = 'Feb'
centroid.names$New[centroid.names$Rows == 'Month3'] = 'Mar'
#This could possibly be slimmed down, but it plots arrows if the variable is continuous (part of the list above)
# and plots a point for the categorical variables instead
for(i in 1:length(summary(cca)$biplot[, 1])){
#Test that the row name is one of the continuous variables before plotting arrows
if(bi.names[i] %in% cont.vars){
arrows(0, 0, summary(cca)$biplot[i, 1], summary(cca)$biplot[i, 2],
lwd = 1, angle = 25, length = 0.10, col = "#F4aa42")
text(summary(cca)$biplot[i, 1] * 1.5,
summary(cca)$biplot[i, 2] * 1.5, labels = bi.names[i], col = '#F4aa42', cex = 0.8, font = 4)
}
}
#now plot the centered mean value of each nominal variable
#Use if statement to test for case where I don't have any categorical variables
if(is.numeric(summary(cca)$centroids) == TRUE){
points(summary(cca)$centroids[, 1] * 0.9, summary(cca)$centroids[, 2] * 0.9, pch = 15, col = 'black')
text(summary(cca)$centroids[, 1] * 0.9, (summary(cca)$centroids[, 2] * 0.9 + 0.15), labels = centroid.names$New,
col = 'darkcyan', cex = 0.7, adj = .5)
}
}
cca.biplot(spe.cca)